A297953 - OEIS

%I #7 Feb 19 2018 14:14:04

%S 1,3,7,13,23,49,99,189,383,777,1531,3061,6167,12289,24531,49197,98351,

%T 196473,393259,786661,1572551,3145585,6292227,12582429,25164767,

%U 50333673,100663387,201322453,402657143,805310689,1610600499,3221229069

%N Number of n X 2 0..1 arrays with every element equal to 1, 2, 4 or 5 king-move adjacent elements, with upper left element zero.

%C Column 2 of A297959.

%H R. H. Hardin, <a href="/A297953/b297953.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) - a(n-2) + 4*a(n-3) - 4*a(n-4) for n>5.

%F Empirical g.f.: (1 + x)*(1 + 2*x^2 - 4*x^3) / ((1 - x)*(1 - 2*x)*(1 + x + 2*x^2)). - _Colin Barker_, Feb 19 2018

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Cf. A297959.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 09 2018