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A299589 Number of n X n 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%I A299589 #7 Apr 19 2020 23:57:34
%S A299589 1,1,5,23,113,576,2583,11656,54738,252959,1159927,5359097,24760544,
%T A299589 114126327,526426848,2429504050,11207820807,51702119063,238537489057,
%U A299589 1100501704736,5077031912807,23422773519432,108060889914594
%N A299589 Number of n X n 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C A299589 Diagonal of A299595.
%H A299589 R. H. Hardin, <a href="/A299589/b299589.txt">Table of n, a(n) for n = 1..70</a>
%F A299589 Empirical: a(n) = 3*a(n-1) +2*a(n-2) +28*a(n-3) -2*a(n-4) -42*a(n-5) -56*a(n-6) +50*a(n-7) -44*a(n-8) +30*a(n-9) -44*a(n-10) +2*a(n-11) +2*a(n-12) -a(n-14) +a(n-15) for n>18.
%e A299589 Some solutions for n=5
%e A299589 ..0..0..0..0..0. .0..0..1..0..0. .0..0..1..0..0. .0..0..0..0..0
%e A299589 ..0..0..0..0..0. .0..0..0..0..1. .0..0..0..0..0. .0..0..0..0..0
%e A299589 ..1..0..0..0..1. .0..0..0..0..0. .0..0..0..0..0. .1..0..0..0..0
%e A299589 ..0..0..0..0..0. .1..0..0..0..0. .0..0..0..0..0. .0..0..0..0..1
%e A299589 ..0..1..0..0..0. .0..0..0..1..0. .0..0..0..1..0. .0..1..0..0..0
%Y A299589 Cf. A299595.
%K A299589 nonn
%O A299589 1,3
%A A299589 _R. H. Hardin_, Feb 13 2018