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%I #12 Apr 28 2021 01:22:34
%S 0,2688,108000,2700432,58038768,1138164048,21063718224,373936700880,
%T 6435143958672,108084508966224,1780281966880656,28856162624878800,
%U 461471700766361616,7295948004100520016,114218818672804436880
%N Number of defective 3-colorings of an n X 5 0..2 array connected diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.
%C Column 5 of A229685.
%H R. H. Hardin, <a href="/A229682/b229682.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 45*a(n-1) - 675*a(n-2) + 2565*a(n-3) + 25272*a(n-4) - 211410*a(n-5) + 3805380*a(n-7) - 8188128*a(n-8) - 14959080*a(n-9) + 70858800*a(n-10) - 85030560*a(n-11) + 34012224*a(n-12) for n > 13.
%F Empirical g.f.: 48*x^2*(56 - 270*x - 7191*x^2 + 52596*x^3 + 88749*x^4 - 1358532*x^5 + 992412*x^6 + 10940832*x^7 - 16886556*x^8 - 22289904*x^9 + 58471632*x^10 - 30233088*x^11) / ((1 - 15*x + 18*x^2)^3*(1 - 18*x^2)^3). - _Colin Barker_, Jun 16 2017
%e Some solutions for n=3:
%e 0 1 0 0 1 0 1 2 1 1 0 1 2 2 2 0 1 2 1 1
%e 1 2 2 2 2 0 0 2 0 0 1 1 1 1 0 2 1 2 2 2
%e 0 2 1 1 1 1 1 2 2 1 2 2 0 2 0 0 1 2 1 0
%K nonn
%O 1,2
%A _R. H. Hardin_, Sep 27 2013
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