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%I #7 Jul 11 2023 07:58:54
%S 24,128,708,3792,20872,114724,631720,3480976,19187324,105781152,
%T 583235304,3215888676,17732499352,97778898080,539167491548,
%U 2973062740752,16394019043496,90399771851092,498482055878472,2748728769087488
%N Number of (n+1) X 3 binary arrays with every 2 X 2 subblock sum equal to some horizontal or vertical neighbor 2 X 2 subblock sum.
%C Column 2 of A185497.
%H R. H. Hardin, <a href="/A185490/b185490.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n)=8*a(n-1)-8*a(n-2)-38*a(n-3)+77*a(n-4)-304*a(n-5)+229*a(n-6)+896*a(n-7)+602*a(n-8)+3542*a(n-9)-1451*a(n-10)-1518*a(n-11)-14971*a(n-12)-30824*a(n-13)-23130*a(n-14)-25773*a(n-15)+40123*a(n-16)+73174*a(n-17)+166738*a(n-18)+101179*a(n-19)+52400*a(n-20)-160962*a(n-21)-297696*a(n-22)-442388*a(n-23)-320904*a(n-24)-33320*a(n-25)+401152*a(n-26)+681440*a(n-27)+823424*a(n-28)+439488*a(n-29)-162240*a(n-30)-562816*a(n-31)-538112*a(n-32)-225024*a(n-33)+151040*a(n-34)+199680*a(n-35)+12288*a(n-36)-36864*a(n-37).
%e Some solutions for 4 X 3
%e ..0..1..0....1..1..1....0..0..1....1..0..1....0..0..0....1..1..1....0..1..0
%e ..1..1..1....0..1..1....1..0..0....1..1..1....1..1..1....1..1..1....1..1..1
%e ..0..1..1....1..1..1....1..0..1....0..1..0....0..1..0....1..0..1....0..0..0
%e ..1..1..1....0..0..0....0..1..0....1..0..1....1..0..1....0..1..0....0..0..0
%Y Cf. A185497.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 29 2011
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