A295914 - OEIS

%I #8 Feb 22 2019 10:04:47

%S 8,28,115,467,1880,7604,30721,124117,501512,2026304,8187195,33079959,

%T 133657824,540037688,2181994609,8816237625,35621557528,143927081684,

%U 581530015059,2349642293451,9493609553944,38358444014860,154985331853649

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

%H R. H. Hardin, <a href="/A295914/b295914.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 7*a(n-2) + 6*a(n-3) - 3*a(n-4) - 4*a(n-5) + a(n-6).

%F Empirical g.f.: x*(8 + 12*x + 3*x^2 - 7*x^3 - 3*x^4 + x^5) / ((1 + x)*(1 - 3*x - 4*x^2 - 2*x^3 + 5*x^4 - x^5)). - _Colin Barker_, Feb 22 2019

%e Some solutions for n=7:

%e ..1..0..0..0. .0..1..0..0. .0..0..0..1. .0..0..0..1. .0..0..0..1

%e ..0..0..1..0. .0..0..0..0. .1..0..0..0. .1..0..0..0. .1..1..0..0

%e ..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..0. .1..1..0..0

%e ..1..1..0..0. .0..0..0..0. .0..1..0..1. .0..0..0..0. .0..0..0..1

%e ..1..1..0..0. .0..0..1..0. .0..0..0..0. .0..0..0..0. .1..0..0..0

%e ..0..0..0..1. .1..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0

%e ..0..0..0..0. .0..0..1..0. .0..0..0..0. .0..0..0..1. .0..1..0..0

%Y Column 4 of A295918.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 29 2017