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%I #8 Oct 25 2018 08:13:34
%S 8,43,212,806,2592,7265,18362,42809,93464,193157,380900,721154,
%T 1317296,2330727,4007402,6713945,10985936,17591423,27613220,42554102,
%U 64469600,96133733,141243690,204670193,292761032,413706065,577972820,798822722
%N Number of 6 X n 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of the elements above it, modulo 3.
%H R. H. Hardin, <a href="/A239033/b239033.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/8640)*n^9 - (61/20160)*n^8 + (263/3360)*n^7 - (1439/1440)*n^6 + (29843/2880)*n^5 - (194227/2880)*n^4 + (668597/2160)*n^3 - (1477657/1680)*n^2 + (59263/42)*n - 943 for n>2.
%F Conjectures from _Colin Barker_, Oct 25 2018: (Start)
%F G.f.: x*(8 - 37*x + 142*x^2 - 339*x^3 + 592*x^4 - 811*x^5 + 996*x^6 - 1020*x^7 + 792*x^8 - 377*x^9 + 88*x^10 + 8*x^11) / (1 - x)^10.
%F a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>12.
%F (End)
%e Some solutions for n=5:
%e ..2..0..0..0..0....2..0..0..0..0....2..0..0..0..0....2..0..0..0..0
%e ..2..0..0..0..0....1..0..0..2..2....2..0..0..0..0....2..0..0..0..0
%e ..1..2..2..0..0....2..0..0..1..2....1..0..0..0..0....1..0..0..0..2
%e ..2..1..1..2..2....2..0..0..0..0....2..0..0..0..0....1..2..2..0..1
%e ..1..2..2..1..2....1..0..2..2..0....1..0..0..2..2....2..1..1..2..2
%e ..1..2..1..0..0....1..2..1..2..1....1..0..0..2..1....1..0..2..1..2
%Y Row 6 of A239030.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 09 2014
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