A268762 - OEIS

%I #8 Jan 14 2019 09:02:09

%S 5,44,223,1148,5170,23156,99057,418924,1736105,7122856,28898144,

%T 116346184,465034573,1848051516,7306228767,28758043956,112751067666,

%U 440538622908,1715952146561,6665380161836,25826102521633,99840968906384

%N Number of n X 4 binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

%H R. H. Hardin, <a href="/A268762/b268762.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + 10*a(n-2) - 32*a(n-3) - 47*a(n-4) + 40*a(n-5) + 38*a(n-6) - 12*a(n-7) - 9*a(n-8).

%F Empirical g.f.: x*(5 + 24*x - 3*x^2 - 24*x^3 - 9*x^4) / (1 - 2*x - 7*x^2 + 2*x^3 + 3*x^4)^2. - _Colin Barker_, Jan 14 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 4 of A268766.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 13 2016