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Search: a203355 -id:a203355
Displaying 1-8 of 8 results found.
page 1
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A203348
Number of (n+2)X3 binary arrays avoiding patterns 010 and 101 in rows, columns and nw-to-se diagonals
+10
1
80, 244, 702, 2062, 6032, 17614, 51482, 150462, 439760, 1285280, 3756472, 10979006, 32088238, 93784004, 274101634, 801114300, 2341409322, 6843215284, 20000601752, 58455572974, 170847560198, 499334577370, 1459400531498, 4265376378604
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 1 of A203355
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 3*a(n-1) +a(n-2) -3*a(n-3) -a(n-4) -2*a(n-5) -a(n-6) +2*a(n-7) +a(n-8) +a(n-9) -2*a(n-11) -a(n-12)
EXAMPLE
Some solutions for n=3
..0..0..1....0..0..1....0..0..0....1..1..0....1..0..0....0..0..1....0..0..1
..0..0..1....0..0..1....1..1..1....1..0..0....1..1..1....0..0..0....0..0..1
..1..0..0....1..1..1....1..1..1....1..0..0....1..1..1....1..0..0....1..0..0
..1..1..0....1..1..1....1..0..0....0..0..0....1..1..1....1..0..0....1..1..0
..1..1..1....1..0..0....1..0..0....0..0..0....0..0..1....1..0..0....0..1..1
KEYWORD
nonn
AUTHOR
R. H. Hardin Dec 31 2011
STATUS
approved
A203349
Number of (n+2)X4 binary arrays avoiding patterns 010 and 101 in rows, columns and nw-to-se diagonals
+10
1
244, 998, 3716, 14068, 53354, 201506, 761710, 2880986, 10892888, 41189884, 155750096, 588937240, 2226948992, 8420752636, 31841355064, 120401617098, 455274228532, 1721526894432, 6509603831244, 24614743024468, 93075644971226
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 2 of A203355
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 5*a(n-1) -2*a(n-2) -10*a(n-3) -a(n-4) +3*a(n-5) +6*a(n-6) +9*a(n-7) +47*a(n-8) -54*a(n-9) -107*a(n-10) +152*a(n-11) +159*a(n-12) -177*a(n-13) -118*a(n-14) +227*a(n-15) +122*a(n-16) -174*a(n-17) -189*a(n-18) +47*a(n-19) +159*a(n-20) -20*a(n-21) -151*a(n-22) -92*a(n-23) -18*a(n-24) +20*a(n-25) +22*a(n-26) +9*a(n-27) +a(n-28) -a(n-29) -a(n-30) for n>31
EXAMPLE
Some solutions for n=3
..0..1..1..0....0..0..1..1....0..0..0..0....1..1..1..0....0..0..0..0
..0..1..1..0....0..0..0..0....0..0..0..0....1..1..0..0....0..0..0..1
..1..1..1..0....0..0..0..0....0..0..1..1....1..0..0..0....1..1..1..1
..1..1..1..0....1..0..0..0....0..1..1..1....1..0..0..0....1..1..1..1
..0..0..0..1....1..0..0..0....0..1..1..1....1..0..0..0....1..1..1..0
KEYWORD
nonn
AUTHOR
R. H. Hardin Dec 31 2011
STATUS
approved
A203350
Number of (n+2)X5 binary arrays avoiding patterns 010 and 101 in rows, columns and nw-to-se diagonals
+10
1
702, 3716, 17676, 84322, 403624, 1933250, 9252084, 44314952, 212152082, 1015748354, 4863391460, 23285377744, 111488661552, 533799347054, 2555788403334, 12236920029664, 58589438107390, 280521733711996
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 3 of A203355
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 8*a(n-1) -12*a(n-2) -24*a(n-3) +17*a(n-4) +88*a(n-5) +102*a(n-6) -243*a(n-7) +99*a(n-8) -772*a(n-9) -1701*a(n-10) +4240*a(n-11) +5897*a(n-12) -4277*a(n-13) -8679*a(n-14) -15973*a(n-15) -19012*a(n-16) +96695*a(n-17) +119498*a(n-18) -305186*a(n-19) -345693*a(n-20) +635898*a(n-21) +828058*a(n-22) -887645*a(n-23) -1637071*a(n-24) +656825*a(n-25) +2571635*a(n-26) +552766*a(n-27) -2937429*a(n-28) -2698824*a(n-29) +1771258*a(n-30) +4613722*a(n-31) +1104975*a(n-32) -4477496*a(n-33) -4207415*a(n-34) +1266663*a(n-35) +4309165*a(n-36) +2221082*a(n-37) -1120602*a(n-38) -2287492*a(n-39) -1232173*a(n-40) +270494*a(n-41) +860200*a(n-42) +589509*a(n-43) +109566*a(n-44) -180687*a(n-45) -220729*a(n-46) -109731*a(n-47) +10788*a(n-48) +55399*a(n-49) +34551*a(n-50) +4495*a(n-51) -8678*a(n-52) -6347*a(n-53) -1159*a(n-54) +1095*a(n-55) +910*a(n-56) +169*a(n-57) -108*a(n-58) -109*a(n-59) -11*a(n-60) +9*a(n-61) +7*a(n-62) +a(n-63) -a(n-64)
EXAMPLE
Some solutions for n=3
..1..1..0..0..1....0..1..1..1..0....1..1..1..1..0....0..1..1..0..0
..1..1..0..0..1....0..1..1..1..0....0..1..1..0..0....0..1..1..1..0
..1..1..0..0..0....0..0..1..1..1....0..0..0..0..0....1..1..1..1..1
..1..0..0..0..0....1..0..0..0..1....0..0..0..0..0....1..1..1..1..1
..1..0..0..0..1....1..0..0..0..0....0..0..1..1..1....0..0..1..1..0
KEYWORD
nonn
AUTHOR
R. H. Hardin Dec 31 2011
STATUS
approved
A203351
Number of (n+2)X6 binary arrays avoiding patterns 010 and 101 in rows, columns and nw-to-se diagonals
+10
1
2062, 14068, 84322, 505798, 3056040, 18480372, 111589592, 674322800, 4074139940, 24612093494, 148701447448, 898399743424, 5427755036698, 32792496406138, 198119766704856, 1196964769857880, 7231611525811128, 43690672868090104
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 4 of A203355
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
EXAMPLE
Some solutions for n=3
..1..0..0..0..0..0....1..0..0..1..1..1....1..1..1..0..0..0....1..0..0..0..1..1
..1..1..0..0..0..0....1..1..1..1..1..0....0..1..1..1..1..0....1..1..0..0..1..1
..1..1..1..0..0..0....1..1..1..1..1..0....0..1..1..1..1..1....0..1..1..0..0..1
..1..1..1..1..1..0....1..1..1..1..1..0....0..0..1..1..1..1....0..1..1..0..0..1
..0..0..1..1..1..1....1..0..0..0..1..1....0..0..0..0..0..0....1..1..1..0..0..0
KEYWORD
nonn
AUTHOR
R. H. Hardin Dec 31 2011
STATUS
approved
A203352
Number of (n+2)X7 binary arrays avoiding patterns 010 and 101 in rows, columns and nw-to-se diagonals
+10
1
6032, 53354, 403624, 3056040, 23451600, 179906536, 1376241620, 10535519936, 80677265034, 617694879242, 4729619887676, 36214315667508, 277281869263340, 2123094465259698, 16256129560983932, 124469811916675344
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 5 of A203355
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
EXAMPLE
Some solutions for n=2
..1..1..1..0..0..0..0....1..0..0..1..1..0..0....1..0..0..1..1..0..0
..1..1..1..1..1..1..0....1..0..0..1..1..1..0....0..1..1..1..1..0..0
..0..1..1..1..1..1..1....1..0..0..0..1..1..0....0..1..1..1..1..0..0
..0..0..0..0..0..0..1....0..0..0..0..0..0..1....0..1..1..1..0..0..0
KEYWORD
nonn
AUTHOR
R. H. Hardin Dec 31 2011
STATUS
approved
A203353
Number of (n+2)X8 binary arrays avoiding patterns 010 and 101 in rows, columns and nw-to-se diagonals
+10
1
17614, 201506, 1933250, 18480372, 179906536, 1749952542, 16952701994, 164412250764, 1595394864290, 15477715431252, 150154793125198, 1456781066059562, 14133076211655868, 137114272202478152
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 6 of A203355
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
EXAMPLE
Some solutions for n=1
..0..0..0..0..0..1..1..1....0..0..0..0..1..1..1..0....1..1..1..0..0..1..1..1
..0..1..1..0..0..0..1..1....1..0..0..0..0..0..1..1....0..0..0..0..0..0..1..1
..1..1..1..1..1..0..0..1....1..1..1..1..0..0..0..1....0..0..0..0..0..0..0..0
KEYWORD
nonn
AUTHOR
R. H. Hardin Dec 31 2011
STATUS
approved
A203354
Number of (n+2)X9 binary arrays avoiding patterns 010 and 101 in rows, columns and nw-to-se diagonals
+10
1
51482, 761710, 9252084, 111589592, 1376241620, 16952701994, 207766349392, 2550416901394, 31330781250354, 384725422513602, 4723941268587528, 58010195343386780, 712359423754591476, 8747629700874450780
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 7 of A203355
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
EXAMPLE
Some solutions for n=1
..0..0..1..1..1..1..1..1..1....0..0..0..0..0..1..1..1..1
..0..0..0..1..1..1..1..1..1....0..0..0..1..1..1..1..1..1
..1..0..0..0..1..1..0..0..1....0..1..1..1..1..1..1..0..0
KEYWORD
nonn
AUTHOR
R. H. Hardin Dec 31 2011
STATUS
approved
A203347
Number of (n+2)X(n+2) binary arrays avoiding patterns 010 and 101 in rows, columns and nw-to-se diagonals
+10
0
80, 998, 17676, 505798, 23451600, 1749952542, 207766349392, 39642112566362, 12152648421141966, 5965344860666094878
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Diagonal of A203355
LINKS
Table of n, a(n) for n=1..10.
EXAMPLE
Some solutions for n=3
..0..1..1..0..0....0..1..1..1..0....0..0..1..1..0....0..1..1..0..0
..1..1..1..1..0....0..0..0..0..0....0..0..1..1..0....0..1..1..1..1
..1..1..1..1..0....1..0..0..0..0....0..1..1..1..0....0..1..1..1..1
..1..1..1..1..0....1..0..0..0..0....0..1..1..1..1....0..0..1..1..0
..1..1..0..0..0....1..0..0..0..0....0..0..1..1..1....0..0..0..0..0
KEYWORD
nonn
AUTHOR
R. H. Hardin Dec 31 2011
STATUS
approved
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