Search: a256029 -id:a256029
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A256022
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Number of (n+2) X (1+2) 0..1 arrays with no 3 x 3 subblock diagonal sum 0 or 1 and no antidiagonal sum 0 or 1 and no row sum 1 and no column sum 1.
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33, 68, 154, 352, 798, 1804, 4086, 9304, 21194, 48176, 109506, 249120, 566754, 1289056, 2931842, 6668688, 15168650, 34502104, 78476674, 178499728, 406009530, 923494792, 2100545026, 4777818256, 10867446266, 24718685528, 56224184050
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OFFSET
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1,1
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LINKS
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FORMULA
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Empirical: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) -2*a(n-6) -4*a(n-7) +2*a(n-9) for n>10.
Empirical g.f.: x*(33 + 2*x + 51*x^2 - 20*x^3 - 24*x^4 - 56*x^5 - 66*x^6 + 12*x^7 + 36*x^8 + 2*x^9) / ((1 - x)*(1 - x - 4*x^3 - 4*x^4 - 4*x^5 - 2*x^6 + 2*x^7 + 2*x^8)). - Colin Barker, Dec 20 2018
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EXAMPLE
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Some solutions for n=4:
..1..0..1....0..1..1....0..1..1....1..1..0....0..1..1....1..1..1....1..1..1
..1..1..1....1..1..0....1..1..1....1..1..1....1..1..1....1..0..1....1..1..1
..1..1..0....1..1..1....1..0..1....1..1..1....1..1..1....1..1..1....1..0..1
..0..1..1....1..1..1....1..1..1....1..1..0....0..1..1....1..1..0....1..1..1
..1..1..1....0..1..1....1..1..1....0..1..1....1..1..1....0..1..1....0..1..1
..1..0..1....1..1..1....1..0..1....1..1..1....1..0..1....1..0..1....1..1..0
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A256028
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Number of (n+2)X(7+2) 0..1 arrays with no 3x3 subblock diagonal sum 0 or 1 and no antidiagonal sum 0 or 1 and no row sum 1 and no column sum 1
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4086, 27424, 223901, 1736085, 13744343, 111505109, 904174706, 7347151637, 59890010020, 487874115891, 3973213543601, 32378167050225, 263909697253124, 2150815427720611, 17528000535815815, 142850512088398850
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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Some solutions for n=2
..1..1..1..1..1..1..1..1..1....0..1..1..1..1..1..1..1..1
..0..1..1..1..1..1..1..1..1....0..1..1..1..1..1..1..0..1
..1..1..1..1..1..1..1..1..0....0..1..1..1..1..0..1..1..1
..1..1..1..1..1..1..1..0..1....0..1..1..0..1..1..1..1..1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A256027
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Number of (n+2)X(6+2) 0..1 arrays with no 3x3 subblock diagonal sum 0 or 1 and no antidiagonal sum 0 or 1 and no row sum 1 and no column sum 1
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+0
1
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1804, 9820, 65202, 408233, 2608924, 17064206, 111505109, 730298893, 4797270283, 31486421742, 206635131614, 1357044255580, 8913054489558, 58531741918910, 384382982272254, 2524426603214310, 16579200749433316, 108882973386998444
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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Some solutions for n=3
..1..1..1..1..0..1..1..1....1..0..1..1..1..1..1..1....1..1..1..1..1..1..0..1
..1..1..0..1..1..1..1..0....1..1..1..1..1..1..0..1....0..1..1..1..0..1..1..0
..1..1..1..1..1..1..1..1....1..1..1..1..1..1..1..1....1..1..1..1..1..1..1..1
..1..1..1..1..1..1..1..1....0..1..1..0..1..1..1..1....1..0..1..1..1..1..1..1
..1..0..1..1..1..1..0..1....1..1..1..1..1..1..0..1....1..1..1..1..1..1..1..1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A256026
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Number of (n+2)X(5+2) 0..1 arrays with no 3x3 subblock diagonal sum 0 or 1 and no antidiagonal sum 0 or 1 and no row sum 1 and no column sum 1
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1
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798, 3500, 18881, 96363, 494704, 2608924, 13744343, 72433360, 383085494, 2025211622, 10699107204, 56559043253, 299094636689, 1581405435044, 8360604894932, 44203749793706, 233723001457450, 1235776972463585
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical recurrence of order 77 (see link above)
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EXAMPLE
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Some solutions for n=4
..0..1..1..0..1..1..1....1..0..1..1..1..1..0....1..1..1..1..1..1..0
..1..1..1..1..1..1..1....0..1..1..1..1..1..0....0..1..1..1..1..1..1
..1..1..1..1..1..1..1....1..1..1..1..1..1..0....1..1..1..0..1..1..1
..1..1..0..1..1..0..1....1..1..1..1..1..1..0....1..1..1..1..1..1..1
..0..1..1..1..1..1..1....1..1..1..1..1..1..0....1..1..1..1..1..1..0
..1..1..1..1..1..1..0....1..1..1..0..1..1..0....1..0..1..1..1..1..1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A256025
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Number of (n+2)X(4+2) 0..1 arrays with no 3x3 subblock diagonal sum 0 or 1 and no antidiagonal sum 0 or 1 and no row sum 1 and no column sum 1
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1
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352, 1302, 5559, 23134, 96363, 408233, 1736085, 7397708, 31551114, 134520680, 573738336, 2448028836, 10444929115, 44562381948, 190130272304, 811234013543, 3461295273878, 14768282266449, 63011902002326, 268853587166114
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 5*a(n-1) -4*a(n-2) +13*a(n-3) -18*a(n-4) -96*a(n-5) -8*a(n-6) -84*a(n-7) +593*a(n-8) +1134*a(n-9) -570*a(n-10) -1366*a(n-11) -2884*a(n-12) -2506*a(n-13) +3113*a(n-14) +7715*a(n-15) +6068*a(n-16) -2862*a(n-17) -12037*a(n-18) -10274*a(n-19) +885*a(n-20) +12618*a(n-21) +12966*a(n-22) +2537*a(n-23) -8366*a(n-24) -10145*a(n-25) -4389*a(n-26) +1648*a(n-27) +3742*a(n-28) +2506*a(n-29) +1283*a(n-30) +466*a(n-31) +34*a(n-32) -344*a(n-33) -560*a(n-34) -449*a(n-35) -277*a(n-36) -94*a(n-37) -10*a(n-38) +10*a(n-39) +8*a(n-40) for n>42
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EXAMPLE
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Some solutions for n=4
..1..1..1..1..1..0....1..1..1..1..1..0....1..1..1..1..1..1....1..1..0..1..1..1
..1..1..1..0..1..1....1..1..0..1..1..1....1..0..1..1..0..1....1..1..1..1..1..1
..1..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..1..1
..1..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..1..1....1..1..0..1..1..0
..1..1..0..1..1..1....1..0..1..1..0..1....1..1..0..1..1..0....1..1..1..1..1..1
..0..1..1..1..1..0....1..1..1..1..1..1....1..1..1..1..0..1....1..1..1..1..1..1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A256024
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Number of (n+2)X(3+2) 0..1 arrays with no 3x3 subblock diagonal sum 0 or 1 and no antidiagonal sum 0 or 1 and no row sum 1 and no column sum 1
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+0
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154, 484, 1689, 5559, 18881, 65202, 223901, 772322, 2674536, 9246717, 31958849, 110567125, 382593936, 1323597069, 4578966412, 15842082720, 54811158663, 189635937913, 656096229235, 2269948418864, 7853573067925, 27171812792714
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 4*a(n-1) -5*a(n-2) +17*a(n-3) -13*a(n-4) -11*a(n-5) -53*a(n-6) -82*a(n-7) +104*a(n-8) +226*a(n-9) +158*a(n-10) -23*a(n-11) -338*a(n-12) -303*a(n-13) -89*a(n-14) +231*a(n-15) +283*a(n-16) +125*a(n-17) -59*a(n-18) -145*a(n-19) -77*a(n-20) -31*a(n-21) +26*a(n-22) +20*a(n-23) +24*a(n-24) +8*a(n-25) +4*a(n-26) for n>28
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EXAMPLE
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Some solutions for n=4
..1..1..0..1..1....1..0..1..1..0....1..0..1..1..0....1..1..1..1..0
..1..1..1..1..1....1..1..1..1..1....1..1..1..1..1....1..1..1..1..1
..1..1..1..1..1....1..1..1..1..1....0..1..1..1..1....1..1..1..1..1
..1..1..1..1..1....1..1..1..1..1....1..1..1..1..1....1..1..0..1..1
..0..1..1..1..0....1..1..1..1..0....1..1..1..1..1....1..1..1..1..0
..1..1..1..0..1....1..1..1..1..1....1..0..1..1..0....1..1..1..0..1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A256023
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Number of (n+2)X(2+2) 0..1 arrays with no 3x3 subblock diagonal sum 0 or 1 and no antidiagonal sum 0 or 1 and no row sum 1 and no column sum 1
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68, 164, 484, 1302, 3500, 9820, 27424, 76068, 212126, 592302, 1651552, 4606638, 12854658, 35865050, 100061478, 279186256, 778969128, 2173402654, 6064060764, 16919528420, 47207600896, 131715146500, 367502127158, 1025377787750
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 3*a(n-1) -a(n-2) +5*a(n-3) -9*a(n-4) -5*a(n-5) -3*a(n-6) +7*a(n-7) +7*a(n-8) +4*a(n-9) -3*a(n-10) -2*a(n-11) -2*a(n-12)
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EXAMPLE
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Some solutions for n=4
..1..0..1..1....1..0..1..1....0..1..1..0....1..1..0..1....1..1..0..1
..1..1..1..1....1..1..1..1....1..1..1..1....0..1..1..1....1..1..1..0
..1..1..0..1....1..1..1..1....1..1..1..1....1..1..1..1....1..1..1..1
..1..1..1..1....0..1..1..0....1..1..0..1....1..1..1..1....0..1..1..1
..1..1..1..0....1..1..1..1....0..1..1..1....1..1..1..0....1..1..1..1
..0..1..1..1....1..1..1..1....1..1..1..0....1..1..0..1....1..1..1..1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A256021
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Number of (n+2)X(n+2) 0..1 arrays with no 3x3 subblock diagonal sum 0 or 1 and no antidiagonal sum 0 or 1 and no row sum 1 and no column sum 1
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33, 164, 1689, 23134, 494704, 17064206, 904174706, 74064844601, 9413114643755, 1840791210516272, 554265737552127281, 257592212385874955248, 184567323274511744214582, 203714031594496792956553885
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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Some solutions for n=4
..0..1..1..1..0..1....0..1..1..1..0..1....1..0..1..1..1..0....1..1..1..1..0..1
..1..1..0..1..1..1....1..1..0..1..1..1....1..1..1..0..1..1....1..1..1..1..1..0
..1..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..1..1
..1..1..1..1..1..0....1..1..1..1..1..1....0..1..1..1..1..1....0..1..1..1..0..1
..1..1..1..1..1..1....0..1..1..0..1..1....1..1..1..1..1..0....1..1..1..1..1..1
..1..1..1..1..1..1....1..1..1..1..1..0....1..1..1..1..1..1....1..0..1..1..1..1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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