A300091 - OEIS

%I #8 May 20 2021 12:25:19

%S 1,7,7,19,35,95,225,575,1563,4179,11555,32259,90327,255307,723255,

%T 2054259,5847519,16660707,47512875,135574255,386984391,1104913059,

%U 3155268051,9011441543,25738758919,73519704603,210007895555,599899095903

%N Number of n X 3 0..1 arrays with every element equal to 0, 2, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Column 3 of A300096.

%H R. H. Hardin, <a href="/A300091/b300091.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) -4*a(n-2) -8*a(n-3) -5*a(n-4) +35*a(n-5) -4*a(n-6) -26*a(n-7) -10*a(n-8) -2*a(n-9) -8*a(n-10) +88*a(n-11) +78*a(n-12) -176*a(n-13) -62*a(n-14) +40*a(n-15) +24*a(n-16) +52*a(n-17) -8*a(n-18) -8*a(n-19) for n > 20.

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A300096.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 24 2018