A298163 - OEIS

%I #7 Mar 23 2018 06:51:20

%S 0,2,2,4,6,11,18,31,53,91,156,269,464,802,1389,2410,4188,7290,12709,

%T 22188,38790,67902,119006,208808,366763,644841,1134799,1998740,

%U 3523204,6214955,10970665,19377607,34246676,60557515,107134803,189622060

%N Number of n X 4 0..1 arrays with every element equal to 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

%C Column 4 of A298167.

%H R. H. Hardin, <a href="/A298163/b298163.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x^2*(2 - 2*x - 2*x^2 - 2*x^3 + x^4 + 2*x^5) / ((1 - x - x^2)*(1 - x - x^2 - x^3 + x^5)). - _Colin Barker_, Mar 23 2018

%e Some solutions for n=8:

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

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

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

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

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

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

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

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

%Y Cf. A298167.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 14 2018