A316927 - OEIS

%I #6 May 24 2021 14:47:51

%S 1,8,25,143,851,5114,31197,191330,1175122,7224809,44437623,273364775,

%T 1681777472,10346885271,63658582520,391658145868,2409675958077,

%U 14825545328503,91214305480541,561197004289508,3452771040560531

%N Number of n X 3 0..1 arrays with every element unequal to 0, 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Column 3 of A316932.

%H R. H. Hardin, <a href="/A316927/b316927.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) -3*a(n-2) -3*a(n-3) -64*a(n-4) -24*a(n-5) +77*a(n-6) +105*a(n-7) +88*a(n-8) -14*a(n-9) -40*a(n-10) +10*a(n-11) +18*a(n-12) +4*a(n-13) for n > 15.

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A316932.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jul 16 2018