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A241126 Number of nX3 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order.

%I A241126 #6 Jul 23 2025 11:10:53
%S A241126 4,54,723,9773,132369,1792237,24269723,328645291,4450319537,
%T A241126 60263615333,816054461063,11050530322615,149639792084929,
%U A241126 2026334190350265,27439427668181531,371568616043522567,5031563999805819365
%N A241126 Number of nX3 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order.
%C A241126 Column 3 of A241130
%H A241126 R. H. Hardin, <a href="/A241126/b241126.txt">Table of n, a(n) for n = 1..210</a>
%F A241126 Empirical: a(n) = 14*a(n-1) -7*a(n-2) +27*a(n-3) -170*a(n-4) -631*a(n-5) -1135*a(n-6) +5278*a(n-7) -3113*a(n-8) +5125*a(n-9) +13678*a(n-10) -10325*a(n-11) +15744*a(n-12) -52520*a(n-13) -13756*a(n-14) -110176*a(n-15) +64424*a(n-16) -53672*a(n-17) -13552*a(n-18) +87456*a(n-19) -198528*a(n-20) +71552*a(n-21) -44288*a(n-22) -116224*a(n-23) -4096*a(n-24) -122880*a(n-25) -65536*a(n-26)
%e A241126 Some solutions for n=4
%e A241126 ..0..1..1....0..1..1....0..1..0....0..1..0....0..1..2....0..1..0....0..1..0
%e A241126 ..1..0..0....2..0..2....2..0..1....1..0..2....0..2..1....0..2..1....1..2..0
%e A241126 ..0..2..1....1..0..2....1..0..1....0..1..0....1..0..2....1..2..1....0..1..1
%e A241126 ..1..2..0....2..1..1....2..1..0....2..1..2....2..0..1....0..1..2....1..2..0
%K A241126 nonn
%O A241126 1,1
%A A241126 _R. H. Hardin_, Apr 16 2014