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A300177 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.

%I A300177 #16 Jun 29 2018 18:18:30
%S A300177 4,32,255,2033,16208,129217,1030173,8212978,65477359,522013397,
%T A300177 4161713160,33178950053,264516722873,2108839989442,16812570686523,
%U A300177 134036975068993,1068599860225264,8519333271178937,67919753770243365
%N A300177 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 A300177 Column 3 of A300182.
%H A300177 R. H. Hardin, <a href="/A300177/b300177.txt">Table of n, a(n) for n = 1..210</a>
%H A300177 Simon Plouffe, <a href="http://vixra.org/abs/1409.0048"> Conjectures of the OEIS, as of June 20, 2018.</a>
%F A300177 Empirical: a(n) = 7*a(n-1) +7*a(n-2) +6*a(n-3).
%F A300177 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 A300177 Some solutions for n=5
%e A300177 ..0..1..1. .0..1..1. .0..0..0. .0..1..1. .0..1..0. .0..0..1. .0..0..1
%e A300177 ..1..1..0. .0..0..1. .0..1..1. .1..1..0. .0..1..1. .0..0..1. .1..1..0
%e A300177 ..1..1..1. .0..0..0. .0..1..0. .0..0..0. .1..0..0. .1..1..0. .0..1..0
%e A300177 ..0..0..1. .0..1..1. .0..0..0. .1..1..1. .1..1..1. .0..0..1. .0..1..1
%e A300177 ..1..0..0. .0..1..1. .1..1..0. .0..0..1. .1..0..1. .0..0..0. .0..0..0
%Y A300177 Cf. A300182.
%K A300177 nonn
%O A300177 1,1
%A A300177 _R. H. Hardin_, Feb 27 2018