A300177 - OEIS

%I #16 Jun 29 2018 18:18:30

%S 4,32,255,2033,16208,129217,1030173,8212978,65477359,522013397,

%T 4161713160,33178950053,264516722873,2108839989442,16812570686523,

%U 134036975068993,1068599860225264,8519333271178937,67919753770243365

%N Number of nX3 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Column 3 of A300182.

%H R. H. Hardin, <a href="/A300177/b300177.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) = 7*a(n-1) +7*a(n-2) +6*a(n-3).

%F Empirical g.f.: -x*(-3*x^2-4*x-4)/(-6*x^3-7*x^2-7*x+1). - _Simon Plouffe_, Jun 21 2018

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A300182.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 27 2018