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A231972 Number of (n+1)X(3+1) 0..1 arrays with no element having a strict majority of its horizontal and vertical neighbors equal to one.

%I A231972 #6 Jul 23 2025 06:45:49
%S A231972 36,169,841,4489,24964,136900,741321,4024036,21911761,119268241,
%T A231972 648771841,3529072836,19199427844,104453715249,568259668900,
%U A231972 3091481744121,16818570092025,91498158928089,497777418977476
%N A231972 Number of (n+1)X(3+1) 0..1 arrays with no element having a strict majority of its horizontal and vertical neighbors equal to one.
%C A231972 Column 3 of A231977
%H A231972 R. H. Hardin, <a href="/A231972/b231972.txt">Table of n, a(n) for n = 1..210</a>
%F A231972 Empirical: a(n) = 2*a(n-1) +8*a(n-2) +36*a(n-3) +90*a(n-4) +170*a(n-5) +66*a(n-6) -303*a(n-7) -268*a(n-8) +124*a(n-9) +40*a(n-10) -200*a(n-11) -184*a(n-12) -96*a(n-13) +57*a(n-14) +146*a(n-15) +36*a(n-16) -4*a(n-17) +22*a(n-18) -10*a(n-19) +6*a(n-20) -a(n-21)
%e A231972 Some solutions for n=2
%e A231972 ..0..0..0..0....0..0..1..1....1..0..0..0....0..0..0..0....0..1..1..0
%e A231972 ..1..0..0..0....0..0..0..0....0..0..1..0....1..0..1..0....0..0..0..0
%e A231972 ..0..0..1..1....1..1..0..0....0..0..0..0....0..0..1..0....1..1..0..0
%K A231972 nonn
%O A231972 1,1
%A A231972 _R. H. Hardin_, Nov 16 2013