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.

0, 2688, 108000, 2700432, 58038768, 1138164048, 21063718224, 373936700880, 6435143958672, 108084508966224, 1780281966880656, 28856162624878800, 461471700766361616, 7295948004100520016, 114218818672804436880

Offset

1,2

Comments

Column 5 of A229685.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

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.

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

Example

Some solutions for n=3:
  0 1 0 0 1      0 1 2 1 1      0 1 2 2 2      0 1 2 1 1
  1 2 2 2 2      0 0 2 0 0      1 1 1 1 0      2 1 2 2 2
  0 2 1 1 1      1 1 2 2 1      2 2 0 2 0      0 1 2 1 0

Crossrefs

Sequence in context: A233899 A350184 A186833 * A186937 A185748 A252404

Adjacent sequences: A229679 A229680 A229681 * A229683 A229684 A229685

Keyword

nonn

Author

R. H. Hardin, Sep 27 2013

Status

approved