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Search: a295379 -id:a295379
Displaying 1-6 of 6 results found.
page 1
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A295374
Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2 or 4 1s.
+10
1
5, 19, 74, 278, 1067, 4071, 15557, 59407, 226944, 866828, 3311093, 12647369, 48309585, 184528995, 704849914, 2692330642, 10283957167, 39281862695, 150045822457, 573133422103, 2189210714608, 8362177726832, 31941199613977
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 3*a(n-1) + 4*a(n-2) - 3*a(n-3) + a(n-4) - 8*a(n-5) - 3*a(n-6) + 5*a(n-7) - 2*a(n-8) + a(n-9) + a(n-10).
Empirical g.f.: x*(5 + 4*x - 3*x^2 - 5*x^3 - 11*x^4 + x^5 + 3*x^6 - x^7 + 2*x^8 + x^9) / (1 - 3*x - 4*x^2 + 3*x^3 - x^4 + 8*x^5 + 3*x^6 - 5*x^7 + 2*x^8 - x^9 - x^10). - Colin Barker, Feb 22 2019
EXAMPLE
Some solutions for n=7:
..0..0..1. .0..1..0. .0..0..1. .0..1..0. .0..1..0. .1..0..1. .1..0..1
..0..1..0. .0..0..1. .0..0..0. .1..0..1. .1..0..0. .0..1..0. .0..0..0
..0..0..0. .1..1..0. .0..0..0. .0..0..0. .0..0..0. .1..0..0. .0..1..0
..0..0..1. .1..1..1. .0..1..0. .1..0..0. .1..0..1. .0..0..0. .0..0..0
..0..0..0. .0..1..1. .0..0..0. .0..1..0. .0..1..0. .1..0..0. .0..1..0
..0..0..1. .0..0..0. .0..1..1. .0..0..0. .0..0..0. .0..1..0. .1..0..1
..0..1..0. .0..0..0. .0..1..1. .1..0..1. .1..0..0. .1..0..1. .0..1..0
CROSSREFS
Column 3 of A295379.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 21 2017
STATUS
approved
A295375
Number of nX4 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2 or 4 1s.
+10
1
8, 48, 278, 1634, 9507, 55643, 325134, 1900380, 11107738, 64922149, 379465246, 2217922765, 12963500193, 75770103923, 442867155601, 2588505603384, 15129505035474, 88430145882513, 516863613785631, 3021005935526290
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 4 of A295379.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 6*a(n-1) +a(n-2) -10*a(n-3) -8*a(n-4) +30*a(n-5) -155*a(n-6) +161*a(n-7) -111*a(n-8) +29*a(n-9) +18*a(n-10) +263*a(n-11) -294*a(n-12) +267*a(n-13) -52*a(n-14) -4*a(n-15) -83*a(n-16) -42*a(n-17) +41*a(n-18) -62*a(n-19) -16*a(n-20) +18*a(n-21) +17*a(n-22) +3*a(n-23) +a(n-24) -a(n-25)
EXAMPLE
Some solutions for n=6
..1..0..0..0. .1..0..0..0. .0..0..1..0. .1..0..0..0. .1..0..0..0
..0..1..0..0. .0..0..1..0. .1..0..0..0. .0..0..0..0. .0..1..1..0
..0..0..0..1. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..1..1..0
..0..0..0..0. .0..1..1..0. .1..0..1..0. .1..0..1..1. .0..0..0..0
..0..0..0..0. .0..1..1..1. .0..1..0..0. .0..0..1..1. .1..1..0..0
..0..1..0..1. .1..0..1..1. .0..0..0..1. .0..1..0..0. .1..1..0..0
CROSSREFS
Cf. A295379.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 21 2017
STATUS
approved
A295376
Number of nX5 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2 or 4 1s.
+10
1
13, 120, 1067, 9507, 85310, 761795, 6819658, 60996884, 545729054, 4882126696, 43677489614, 390749347628, 3495770832651, 31274176146411, 279788295651612, 2503069579137149, 22393213414231715, 200336400920779459
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 5 of A295379.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 70
FORMULA
Empirical recurrence of order 70 (see link above)
EXAMPLE
Some solutions for n=5
..0..0..1..0..0. .0..0..1..0..0. .1..0..0..1..0. .1..1..1..0..0
..0..0..0..0..1. .0..1..0..0..1. .0..0..0..0..0. .1..0..1..0..1
..1..1..0..0..0. .1..0..1..0..0. .1..0..0..1..1. .1..0..1..1..0
..1..1..0..0..0. .0..1..0..0..0. .0..0..0..1..1. .1..0..0..1..0
..0..0..0..0..1. .0..0..0..0..0. .0..0..0..0..0. .1..1..1..1..0
CROSSREFS
Cf. A295379.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 21 2017
STATUS
approved
A295377
Number of nX6 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2 or 4 1s.
+10
1
21, 299, 4071, 55643, 761795, 10437240, 142860055, 1956512289, 26790134422, 366852068404, 5023461594972, 68788552129955, 941953214288271, 12898594994181355, 176626393130327608, 2418626153744793468
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 6 of A295379.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
EXAMPLE
Some solutions for n=4
..0..0..0..0..0..0. .0..0..0..1..0..0. .1..0..0..0..0..0. .0..1..0..1..1..0
..0..0..0..0..0..0. .0..0..0..0..0..0. .0..0..1..0..0..0. .1..0..1..1..1..0
..0..0..1..0..0..1. .1..0..1..0..1..0. .0..0..0..0..0..0. .0..0..1..1..0..0
..0..1..0..0..1..0. .0..1..0..1..0..1. .0..0..0..0..0..0. .0..0..0..0..1..0
CROSSREFS
Cf. A295379.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 21 2017
STATUS
approved
A295378
Number of nX7 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2 or 4 1s.
+10
1
34, 747, 15557, 325134, 6819658, 142860055, 2995361770, 62765357574, 1315649551906, 27574133240044, 577944446997342, 12113314594045600, 253888394444548265, 5321347134853621559, 111532355602550043873
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 7 of A295379.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
EXAMPLE
Some solutions for n=3
..0..0..1..1..0..0..1. .0..0..0..1..0..0..0. .0..0..0..0..0..1..0
..0..1..1..1..0..1..0. .0..0..1..0..1..0..1. .0..0..0..0..0..0..0
..0..1..1..0..1..0..0. .1..0..0..0..0..0..0. .0..1..0..1..0..0..1
CROSSREFS
Cf. A295379.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 21 2017
STATUS
approved
A295373
Number of n X n 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2 or 4 1's.
+10
0
2, 8, 74, 1634, 85310, 10437240, 2995361770, 2013609204094, 3172028798241544, 11706071393300493820, 101212810609370065235246, 2050164710762566420019514822
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Diagonal of A295379.
LINKS
Table of n, a(n) for n=1..12.
EXAMPLE
Some solutions for n=5
..0..1..0..0..0. .0..0..0..1..0. .0..0..0..0..0. .0..0..1..1..0
..0..0..0..1..0. .1..0..0..0..0. .0..0..1..0..1. .1..0..1..1..1
..0..0..1..0..0. .0..1..0..1..0. .0..1..0..1..0. .0..0..0..1..1
..0..0..0..0..0. .1..0..1..0..0. .0..0..0..0..0. .0..0..0..0..0
..0..0..1..0..1. .0..0..0..1..0. .0..1..0..1..0. .0..0..1..0..0
CROSSREFS
Cf. A295379.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 21 2017
STATUS
approved
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