A298570 - OEIS

%I #6 Jan 01 2024 19:22:43

%S 1,4,1,2,14,10,12,72,82,90,400,600,702,2326,4122,5330,14086,27392,

%T 39040,88320,179170,277358,568600,1165362,1925470,3726194,7580456,

%U 13147134,24677244,49453854,88749136,164309028,323901436,594595204,1096340090

%N Number of n X 3 0..1 arrays with every element equal to 0, 2, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

%C Column 3 of A298575.

%H R. H. Hardin, <a href="/A298570/b298570.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-3) +2*a(n-4) +a(n-5) -10*a(n-6) -2*a(n-7) -2*a(n-8) +2*a(n-9).

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A298575.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 22 2018