cp's OEIS Frontend

A269012 Number of 2 X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

%I A269012 #7 Jan 18 2019 06:33:10
%S A269012 0,4,8,36,88,272,696,1900,4856,12588,31792,80288,200304,498004,
%T A269012 1229672,3024948,7407496,18079664,43980072,106688956,258132824,
%U A269012 623113020,1500935776,3608439104,8659683552,20747930788,49635222728,118576046148
%N A269012 Number of 2 X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.
%H A269012 R. H. Hardin, <a href="/A269012/b269012.txt">Table of n, a(n) for n = 1..210</a>
%F A269012 Empirical: a(n) = 2*a(n-1) + 5*a(n-2) - 6*a(n-3) - 9*a(n-4).
%F A269012 Conjectures from _Colin Barker_, Jan 18 2019: (Start)
%F A269012 G.f.: 4*x^2 / (1 - x - 3*x^2)^2.
%F A269012 a(n) = 4*(-((1/2)*(1+sqrt(13)))^n*(sqrt(13)-13*n) + ((1/2)*(1-sqrt(13)))^n*(sqrt(13)+13*n)) / 169.
%F A269012 (End)
%e A269012 Some solutions for n=4:
%e A269012 ..0..1..0..1. .1..0..0..1. .0..0..1..1. .1..0..1..0. .0..0..0..0
%e A269012 ..1..0..0..0. .0..1..0..1. .0..0..0..0. .0..0..0..1. .0..0..1..1
%Y A269012 Row 2 of A269011.
%K A269012 nonn
%O A269012 1,2
%A A269012 _R. H. Hardin_, Feb 17 2016