A231651 -id:A231651 - cp's OEIS frontend

A231645 Number of n X 2 0..2 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

3, 35, 104, 341, 1189, 4040, 13560, 45803, 155131, 524683, 1773770, 5998876, 20290918, 68629108, 232120783, 785115525, 2655576210, 8982247095, 30381769982, 102764504913, 347595681724, 1175726561166, 3976846922803, 13451535863780

Offset: 1

R. H. Hardin, Nov 12 2013

nonn

Column 2 of A231651.

			Some solutions for n=3:
..1..1....2..2....0..0....1..1....1..2....0..0....0..0....0..0....2..0....0..1
..2..1....1..1....0..2....2..2....0..0....2..1....0..0....0..0....2..0....0..0
..1..1....1..1....0..0....1..1....0..0....0..0....2..1....1..2....0..0....1..0

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A231651.

Empirical: a(n) = 6*a(n-1) - 12*a(n-2) + 19*a(n-3) - 32*a(n-4) + 15*a(n-5) - 13*a(n-6) + 13*a(n-7) + 10*a(n-8) + 7*a(n-9) + 5*a(n-10) + a(n-11) for n>12.

Empirical g.f.: x*(3 + 17*x - 70*x^2 + 80*x^3 - 178*x^4 + 97*x^5 - 49*x^6 + 100*x^7 + 73*x^8 + 48*x^9 + 31*x^10 + 6*x^11) / (1 - 6*x + 12*x^2 - 19*x^3 + 32*x^4 - 15*x^5 + 13*x^6 - 13*x^7 - 10*x^8 - 7*x^9- 5*x^10 - x^11). - Colin Barker, Mar 18 2018

A231646 Number of nX3 0..2 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

Original entry on oeis.org

9, 104, 920, 7682, 61574, 490760, 3929027, 31501117, 252454167, 2022844426, 16209670759, 129896538285, 1040912909763, 8341204621591, 66841228911422, 535624801555647, 4292168448581044, 34394795269925139, 275618732897288063

Offset: 1

R. H. Hardin, Nov 12 2013

nonn

Column 3 of A231651

			Some solutions for n=3
..1..0..0....2..0..0....2..1..1....1..1..2....2..1..0....0..0..0....0..2..1
..1..0..0....0..0..1....2..1..2....1..1..1....2..0..0....0..1..2....0..0..1
..1..1..0....0..2..1....2..1..1....2..2..1....0..0..1....0..1..2....2..0..0

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 18*a(n-1) -133*a(n-2) +640*a(n-3) -2309*a(n-4) +5762*a(n-5) -9918*a(n-6) +8864*a(n-7) +2970*a(n-8) -18151*a(n-9) +23183*a(n-10) +21799*a(n-11) -75109*a(n-12) +56329*a(n-13) -9892*a(n-14) -115814*a(n-15) +105665*a(n-16) +64162*a(n-17) -38348*a(n-18) +8767*a(n-19) +54790*a(n-20) -95246*a(n-21) -139155*a(n-22) +81259*a(n-23) +104482*a(n-24) +18968*a(n-25) -2909*a(n-26) -41630*a(n-27) -37578*a(n-28) +6670*a(n-29) +17693*a(n-30) +5629*a(n-31) -713*a(n-32) -928*a(n-33) -300*a(n-34) -52*a(n-35) -4*a(n-36) for n>37

A231647 Number of nX4 0..2 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

Original entry on oeis.org

22, 341, 7682, 137961, 2412274, 42882766, 765163605, 13643499478, 243317286312, 4340128403053, 77412117578960, 1380680024126767, 24625023800964584, 439200986311182069, 7833405373009045177, 139713294059336266128

Offset: 1

R. H. Hardin, Nov 12 2013

nonn

Column 4 of A231651

			Some solutions for n=3
..1..1..1..1....1..0..0..2....2..1..0..0....0..1..2..1....1..0..0..2
..0..0..2..2....0..0..0..1....0..0..0..0....0..0..0..1....1..0..0..1
..0..0..2..2....0..0..0..1....0..0..2..1....2..0..0..2....1..2..0..0

R. H. Hardin, Table of n, a(n) for n = 1..210

A231648 Number of nX5 0..2 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

Original entry on oeis.org

51, 1189, 61574, 2412274, 96014413, 3936913977, 161357952814, 6602715583511, 270337779895196, 11069019817530645, 453147169968161944, 18550832129905355953, 759448690449540291323, 31091056859424132422442

Offset: 1

R. H. Hardin, Nov 12 2013

nonn

Column 5 of A231651

			Some solutions for n=3
..0..2..1..0..0....0..0..2..2..2....0..0..0..0..0....0..0..0..0..2
..0..0..0..0..2....1..0..0..0..1....1..2..2..0..2....1..0..0..0..0
..1..0..0..0..0....0..0..2..0..0....1..2..2..0..0....2..2..1..0..0

R. H. Hardin, Table of n, a(n) for n = 1..210

A231649 Number of nX6 0..2 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

Original entry on oeis.org

121, 4040, 490760, 42882766, 3936913977, 374409597564, 35384751611050, 3335789961947404, 314852421269523851, 29721381118553717447, 2805039910196136173308, 264733396758705184183618

Offset: 1

R. H. Hardin, Nov 12 2013

nonn

Column 6 of A231651

			Some solutions for n=3
..2..0..0..0..2..2....0..0..0..0..0..0....0..1..2..2..2..1....2..0..0..0..0..0
..0..0..0..0..0..1....0..2..2..0..0..0....0..1..0..0..0..1....0..0..0..0..0..2
..0..2..0..0..0..1....0..2..2..0..0..2....0..1..0..0..0..2....0..2..2..2..2..2

R. H. Hardin, Table of n, a(n) for n = 1..210

A231650 Number of nX7 0..2 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

Original entry on oeis.org

292, 13560, 3929027, 765163605, 161357952814, 35384751611050, 7673178325424236, 1659606986967401246, 359651366294031374125, 77952234653703371179457, 16890753872192197103219139

Offset: 1

R. H. Hardin, Nov 12 2013

nonn

Column 7 of A231651

			Some solutions for n=3
..0..0..2..2..2..2..2....0..0..2..2..0..0..0....0..0..0..0..2..2..1
..0..0..1..1..0..0..2....0..0..2..2..0..1..2....0..0..0..0..0..0..1
..0..0..0..0..0..0..2....0..0..0..0..0..1..1....0..1..0..0..0..0..1

R. H. Hardin, Table of n, a(n) for n = 1..161

A231644 Number of n X n 0..2 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

Original entry on oeis.org

3, 35, 920, 137961, 96014413, 374409597564, 7673178325424236, 823755531731133088630, 468550736330699430524865279

Offset: 1

R. H. Hardin, Nov 12 2013

nonn

Diagonal of A231651

			Some solutions for n=3
..0..0..0....0..2..1....1..1..2....0..0..1....0..2..0....2..0..0....0..0..0
..0..0..2....0..1..1....0..0..1....2..0..1....0..0..0....1..0..0....0..2..1
..1..1..1....0..1..1....0..0..1....1..0..0....0..0..2....1..2..2....0..0..0

cp's OEIS Frontend

A231645 Number of n X 2 0..2 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A231646 Number of nX3 0..2 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

Views

Author

Keywords

Comments

Examples

Links

Formula

A231647 Number of nX4 0..2 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

Views

Author

Keywords

Comments

Examples

Links

A231648 Number of nX5 0..2 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

Views

Author

Keywords

Comments

Examples

Links

A231649 Number of nX6 0..2 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

Views

Author

Keywords

Comments

Examples

Links

A231650 Number of nX7 0..2 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

Views

Author

Keywords

Comments

Examples

Links

A231644 Number of n X n 0..2 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

Views

Author

Keywords

Comments

Examples