A305477 - OEIS

%I #16 Jun 29 2018 19:09:37

%S 3,7,10,21,40,70,125,231,419,752,1365,2482,4488,8121,14729,26689,

%T 48322,87545,158636,287360,520537,943067,1708503,3095024,5606953,

%U 10157742,18401740,33336465,60392685,109407857,198203346,359065917,650486008

%N Number of nX3 0..1 arrays with every element unequal to 0, 1, 3, 6 or 8 king-move adjacent elements, with upper left element zero.

%C Column 3 of A305482.

%H R. H. Hardin, <a href="/A305477/b305477.txt">Table of n, a(n) for n = 1..210</a>

%H Simon Plouffe, <a href="http://vixra.org/abs/1409.0048">Conjectures of the OEIS, as of June 20, 2018.</a>

%F Empirical: a(n) = a(n-1) +3*a(n-3) -2*a(n-6) for n>9.

%F Empirical: -x*(-2*x^8-2*x^6-2*x^4+2*x^3+3*x^2+4*x+3)/(-2*x^6+3*x^3+x-1). - _Simon Plouffe_, Jun 20 2018

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A305482.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jun 02 2018