A296733 - OEIS

%I #7 Feb 25 2019 08:15:56

%S 2,11,31,88,287,881,2686,8347,25763,79376,245227,757045,2336222,

%T 7212287,22263871,68722504,212138639,654844841,2021399374,6239772643,

%U 19261292171,59456768000,183534426499,566544237805,1748839677662,5398414303799

%N Number of n X 2 0..1 arrays with each 1 adjacent to 1, 2 or 4 king-move neighboring 1s.

%H R. H. Hardin, <a href="/A296733/b296733.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) - a(n-2) + 8*a(n-3) - 12*a(n-4) + 2*a(n-5) - 12*a(n-6).

%F Empirical g.f.: x*(2 + x + 2*x^2)*(1 + 2*x - 2*x^2 - 6*x^3) / (1 - 3*x + x^2 - 8*x^3 + 12*x^4 - 2*x^5 + 12*x^6). - _Colin Barker_, Feb 25 2019

%e Some solutions for n=5:

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

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

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

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

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

%Y Column 2 of A296739.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 19 2017