login
Number of n X 2 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0, 2 or 3 neighboring 1s.
1

%I #8 Feb 23 2019 07:24:16

%S 3,9,22,62,172,480,1358,3849,10951,31232,89193,254996,729509,2087983,

%T 5978057,17119192,49030629,140440575,402295454,1152434018,3301409215,

%U 9457817513,27094931531,77622729861,222378228416,637084878266

%N Number of n X 2 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0, 2 or 3 neighboring 1s.

%H R. H. Hardin, <a href="/A296582/b296582.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + a(n-2) - a(n-3) - 8*a(n-4) - 3*a(n-6) - 2*a(n-7) - 5*a(n-8) + a(n-9).

%F Empirical g.f.: x*(3 - 8*x^2 - 10*x^3 - 3*x^4 - 4*x^5 - 7*x^6 - 4*x^7 + x^8) / (1 - 3*x - x^2 + x^3 + 8*x^4 + 3*x^6 + 2*x^7 + 5*x^8 - x^9). - _Colin Barker_, Feb 23 2019

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Column 2 of A296588.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 16 2017