A297945 - OEIS

%I #14 Feb 19 2018 08:26:50

%S 1,4,18,52,174,604,2048,6948,23652,80488,273840,931808,3170824,

%T 10789824,36716272,124940880,425158448,1446762336,4923157280,

%U 16752910976,57008139808,193991844032,660130925440,2246346198336,7644046147776

%N Number of n X 2 0..1 arrays with every element equal to 1, 2, 3 or 5 king-move adjacent elements, with upper left element zero.

%C Column 2 of A297951.

%H R. H. Hardin, <a href="/A297945/b297945.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(1 + 4*x^2 - 14*x^3 + 4*x^5) / (1 - 4*x + 2*x^2 - 2*x^3 + 6*x^4 + 4*x^5). - _Colin Barker_, Feb 18 2018

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Cf. A297951.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 09 2018