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%I #6 May 05 2021 09:52:44
%S 1,5,16,44,159,580,2145,8034,30017,113054,426489,1609240,6078735,
%T 22967236,86790502,328025891,1239827639,4686314366,17713839936,
%U 66957270615,253096517486,956701365708,3616324822124,13669703752446
%N Number of n X 3 0..1 arrays with every element equal to 0, 2, 3, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Column 3 of A300966.
%H R. H. Hardin, <a href="/A300961/b300961.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) +5*a(n-2) +2*a(n-3) -30*a(n-4) -29*a(n-5) -3*a(n-6) +26*a(n-7) +89*a(n-8) +79*a(n-9) -20*a(n-10) -52*a(n-11) -28*a(n-12) +96*a(n-13) +12*a(n-14) +4*a(n-15) -39*a(n-16) -17*a(n-17) -4*a(n-18) -3*a(n-19) +7*a(n-20) -3*a(n-21) +2*a(n-22) for n > 24.
%e Some solutions for n=5
%e ..0..1..1. .0..1..1. .0..0..0. .0..0..1. .0..0..0. .0..1..1. .0..1..1
%e ..1..1..0. .1..1..0. .0..1..0. .0..0..0. .0..1..0. .1..1..0. .1..1..1
%e ..0..1..1. .1..0..0. .0..0..1. .1..0..0. .0..0..0. .1..0..0. .1..1..0
%e ..1..1..1. .0..1..0. .1..0..0. .0..1..0. .1..1..1. .1..1..1. .0..1..1
%e ..1..1..0. .0..0..1. .0..0..0. .0..0..1. .1..1..1. .1..1..0. .1..1..0
%Y Cf. A300966.
%K nonn
%O 1,2
%A _R. H. Hardin_, Mar 17 2018
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