A297883 - OEIS

%I #7 Feb 19 2018 14:05:47

%S 2,7,13,29,69,137,301,705,1461,3193,7373,15729,34405,78569,170813,

%T 374945,849493,1868953,4119725,9284817,20576325,45534025,102285085,

%U 227659265,505431861,1133187833,2528544397,5627807793,12604474149,28165860265

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

%C Column 2 of A297889.

%H R. H. Hardin, <a href="/A297883/b297883.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) - 2*a(n-2) + 8*a(n-3) -  20*a(n-4) + 8*a(n-5) for n>6.

%F Empirical g.f.: x*(2 + x - 4*x^2 - 12*x^3 - 8*x^4 + 8*x^5) / ((1 - 2*x)*(1 - x - 8*x^3 + 4*x^4)). - _Colin Barker_, Feb 19 2018

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Cf. A297889.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 07 2018