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A230751 Number of (n+3)X(2+3) 0..2 arrays 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 A230751 #6 Jul 23 2025 05:59:48
%S A230751 192,5544,178608,4838400,129731328,3423037464,90231813552,
%T A230751 2371911724800,62340751389888,1637784374230152,43026042037169712,
%U A230751 1130254426477308672,29690633338904531712,779934263524825538808,20487845491955757699888
%N A230751 Number of (n+3)X(2+3) 0..2 arrays 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 A230751 Column 2 of A230757
%H A230751 R. H. Hardin, <a href="/A230751/b230751.txt">Table of n, a(n) for n = 1..210</a>
%F A230751 Empirical: a(n) = 31*a(n-1) -3864*a(n-3) +14574*a(n-4) +37518*a(n-5) -238176*a(n-6) +1739072*a(n-7) -6602591*a(n-8) -1491775*a(n-9) +16560784*a(n-10) +89336824*a(n-11) -386330924*a(n-12) -86274348*a(n-13) +1166624784*a(n-14) -2006665968*a(n-15) +6479579969*a(n-16) -3512617823*a(n-17) +540133040*a(n-18) -4346818712*a(n-19) +7862435998*a(n-20) -5792501698*a(n-21) +1019133200*a(n-22) -2919714960*a(n-23) -5125129473*a(n-24) -560243617*a(n-25) +332641792*a(n-26) -444124168*a(n-27) -992749888*a(n-28) +21841536*a(n-29) -8986624*a(n-30) -13069312*a(n-31) -25735168*a(n-32) +1699840*a(n-33) -32768*a(n-35) +262144*a(n-36)
%e A230751 Some solutions for n=1
%e A230751 ..0..0..2..0..2....0..2..2..2..2....0..1..0..1..1....0..2..2..0..2
%e A230751 ..2..1..1..0..2....1..1..0..0..0....0..1..2..2..0....0..1..1..0..2
%e A230751 ..1..1..0..2..1....0..0..0..1..1....2..0..1..2..1....0..1..1..0..2
%e A230751 ..0..2..0..2..1....2..2..2..2..0....2..0..1..0..1....0..2..2..0..2
%K A230751 nonn
%O A230751 1,1
%A A230751 _R. H. Hardin_, Oct 29 2013