A229682 - OEIS

A229682

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.

%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