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

1,1

Comments

Column 2 of A231651.

Links

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

Formula

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

Example

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

Crossrefs

Cf. A231651.

Sequence in context: A334068 A001539 A113854 * A076376 A338787 A353619

Adjacent sequences: A231642 A231643 A231644 * A231646 A231647 A231648

Keyword

nonn

Author

R. H. Hardin, Nov 12 2013

Status

approved