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A299593 Number of n X 6 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%I A299593 #8 Feb 15 2018 20:48:15
%S A299593 13,15,35,121,256,576,1225,2601,5625,12100,25921,55696,119716,257049,
%T A299593 552049,1185921,2547216,5470921,11751184,25240576,54213769,116445681,
%U A299593 250114225,537219684,1153892961,2478446656,5323453444,11434238761
%N A299593 Number of n X 6 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C A299593 Column 6 of A299595.
%H A299593 R. H. Hardin, <a href="/A299593/b299593.txt">Table of n, a(n) for n = 1..210</a>
%F A299593 Empirical: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9.
%F A299593 Empirical g.f.: x*(13 + 2*x + 7*x^2 + 32*x^3 + 42*x^4 + 92*x^5 + 23*x^6 - 39*x^7 - 29*x^8) / ((1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)). - _Colin Barker_, Feb 15 2018
%e A299593 Some solutions for n=5:
%e A299593 ..0..0..0..1..0..0. .0..0..0..0..0..0. .0..0..0..1..0..0. .0..0..0..0..0..0
%e A299593 ..1..0..0..0..0..1. .1..0..0..0..0..1. .1..0..0..0..0..0. .1..0..0..0..0..1
%e A299593 ..0..0..0..0..0..0. .0..0..0..0..0..0. .0..0..0..0..0..0. .0..0..0..0..0..0
%e A299593 ..0..0..0..0..0..0. .0..0..0..0..0..0. .0..0..0..0..0..0. .0..0..0..0..0..0
%e A299593 ..0..1..0..0..0..0. .0..0..1..0..0..0. .0..1..0..0..1..0. .0..1..0..0..1..0
%Y A299593 Cf. A299595.
%K A299593 nonn
%O A299593 1,1
%A A299593 _R. H. Hardin_, Feb 13 2018