A243206 Number of 3-matchings of the n X n grid graph.

0, 0, 0, 56, 1044, 6632, 26172, 78536, 196916, 434584, 871612, 1622552, 2845076, 4749576, 7609724, 11773992, 17678132, 25858616, 36967036, 51785464, 71242772, 96431912, 128628156, 169308296, 220170804, 283156952, 360472892, 454612696, 568382356, 704924744

Offset: 0

Author

Alois P. Heinz, Jun 01 2014

Keywords

• nonn

Comments

Number of ways 3 dominoes can be placed on an n X n chessboard.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=3 of A242861.

Programs

Maple

a:= n-> `if`(n<3, 0, ((((((4*n-12)*n-30)*n+116)*n+14)*n-272)*n+156)/3):
seq(a(n), n=0..40);

Formula

G.f.: 4*x^3*(-14-163*x-125*x^2-5*x^5-6*x^4+72*x^3+x^6)/(x-1)^7.

a(n) = (4*n^6-12*n^5-30*n^4+116*n^3+14*n^2-272*n+156)/3 for n>=3, a(n) = 0 for n<3.