A296034 Number of n X 3 0..1 arrays with each 1 adjacent to 2 or 4 king-move neighboring 1s.

1, 11, 31, 70, 251, 799, 2266, 7005, 21780, 65489, 199273, 610585, 1857468, 5653794, 17249124, 52563162, 160123076, 488054813, 1487412562, 4532419434, 13812563405, 42094180094, 128277984857, 390920465658, 1191319783180, 3630484158342

Offset

1,2

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + a(n-2) + 11*a(n-3) - 7*a(n-4) - 12*a(n-5) - 23*a(n-6) + 19*a(n-8) + 9*a(n-9) - 3*a(n-10) - 2*a(n-11).

Empirical g.f.: x*(1 + 9*x + 8*x^2 - 14*x^3 - 34*x^4 - 25*x^5 + 19*x^6 + 28*x^7 + 6*x^8 - 5*x^9 - 2*x^10) / (1 - 2*x - x^2 - 11*x^3 + 7*x^4 + 12*x^5 + 23*x^6 - 19*x^8 - 9*x^9 + 3*x^10 + 2*x^11). - Colin Barker, Feb 22 2019

Example

Some solutions for n=5:
..0..0..0. .0..0..0. .1..0..1. .0..1..0. .0..0..0. .1..0..1. .0..0..1
..1..0..0. .1..0..0. .1..1..1. .1..1..0. .1..1..0. .1..1..1. .1..1..1
..1..1..0. .1..1..1. .0..0..0. .0..0..0. .1..0..0. .0..0..0. .1..0..0
..1..1..0. .0..0..1. .1..1..0. .1..1..0. .1..1..0. .0..0..0. .1..1..0
..1..0..0. .0..1..1. .1..0..0. .0..1..0. .0..0..0. .0..0..0. .0..0..0

Crossrefs

Column 3 of A296039.

Sequence in context: A090562 A174244 A136061 * A090233 A139836 A085715

Adjacent sequences: A296031 A296032 A296033 * A296035 A296036 A296037

Keyword

nonn

Author

R. H. Hardin, Dec 03 2017

Status

approved