%I #7 Mar 22 2018 12:54:38

%S 1,7,15,25,47,109,245,545,1253,2859,6557,15131,34879,80643,186663,

%T 432253,1002043,2323805,5391149,12511905,29043489,67430735,156577101,

%U 363614071,844480819,1961394067,4555748943,10582066605,24580613559,57098398457

%N Number of n X 3 0..1 arrays with every element equal to 1, 2, 4 or 5 king-move adjacent elements, with upper left element zero.

%C Column 3 of A297959.

%H R. H. Hardin, <a href="/A297954/b297954.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 2*a(n-2) + a(n-3) - 8*a(n-4) - 2*a(n-5) - 2*a(n-6) + 2*a(n-7) - a(n-8) + 2*a(n-9) + 3*a(n-11) + 2*a(n-12) for n>13.

%F Empirical g.f.: x*(1 - 2*x)*(1 + 7*x + 13*x^2 + 6*x^3 - 20*x^4 - 32*x^5 - 20*x^6 - 8*x^7 - 9*x^8 - 9*x^9 - 7*x^10 - 2*x^11) / ((1 - x)*(1 - x - 3*x^2 - 4*x^3 + 4*x^4 + 6*x^5 + 8*x^6 + 6*x^7 + 7*x^8 + 5*x^9 + 5*x^10+ 2*x^11)). - _Colin Barker_, Mar 22 2018

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Cf. A297959.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 09 2018