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A230737 Number of (n+3)X(4+3) 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

%I A230737 #6 Jul 23 2025 05:59:14
%S A230737 102,2016,16536,320970,2382398,46599682,342031378,6692078688,
%T A230737 49068380730,959928337654,7037607186036,137677370665624,
%U A230737 1009342929539188,19745940646875492,144761390761971996,2831990839783724564
%N A230737 Number of (n+3)X(4+3) 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.
%C A230737 Column 4 of A230739
%H A230737 R. H. Hardin, <a href="/A230737/b230737.txt">Table of n, a(n) for n = 1..210</a>
%F A230737 Empirical: a(n) = 185*a(n-2) -6851*a(n-4) +145707*a(n-6) -2849231*a(n-8) +30720183*a(n-10) -36007996*a(n-12) -743385180*a(n-14) +287330815*a(n-16) +8627923017*a(n-18) -12118273932*a(n-20) -29408445279*a(n-22) +45675171837*a(n-24) -13807146112*a(n-26) -2411662568755*a(n-28) +3802259458200*a(n-30) +3456476952882*a(n-32) +4249525502473*a(n-34) -5769431443156*a(n-36) -7037014662528*a(n-38) +2632063276930*a(n-40) +18416679443602*a(n-42) +9430615399362*a(n-44) +259673859628*a(n-46) +64576080600*a(n-48) +325261872*a(n-50)
%e A230737 Some solutions for n=3
%e A230737 ..x..0..x..1..x..1..x....x..0..x..0..x..0..x....x..0..x..1..x..1..x
%e A230737 ..1..x..0..x..2..x..2....2..x..1..x..1..x..1....1..x..0..x..2..x..2
%e A230737 ..x..2..x..2..x..0..x....x..2..x..0..x..2..x....x..2..x..2..x..0..x
%e A230737 ..2..x..1..x..1..x..2....1..x..0..x..0..x..1....0..x..2..x..1..x..2
%e A230737 ..x..0..x..0..x..1..x....x..0..x..1..x..2..x....x..1..x..0..x..1..x
%e A230737 ..2..x..2..x..0..x..0....2..x..2..x..0..x..1....0..x..2..x..2..x..0
%K A230737 nonn
%O A230737 1,1
%A A230737 _R. H. Hardin_, Oct 28 2013