A297427 - OEIS

%I #8 Feb 28 2019 18:51:55

%S 1,12,26,42,183,513,1085,3332,9744,23836,65693,187681,491757,1322824,

%T 3682514,9913750,26662827,73102697,198448393,535843320,1459128416,

%U 3966961416,10743629897,29183372609,79314611625,215140998420

%N Number of n X 4 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2 neighboring 1s.

%H R. H. Hardin, <a href="/A297427/b297427.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 12*a(n-3) + 2*a(n-4) + 2*a(n-5) - 7*a(n-6) - a(n-7).

%F Empirical g.f.: x*(1 + 11*x + 14*x^2 + 4*x^3 - 5*x^4 - 8*x^5 - x^6) / (1 - x - 12*x^3 - 2*x^4 - 2*x^5 + 7*x^6 + x^7). - _Colin Barker_, Feb 28 2019

%e Some solutions for n=5:

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

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

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

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

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

%Y Column 4 of A297431.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 30 2017