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

0,4

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

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.

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);

Crossrefs

Column k=3 of A242861.

Sequence in context: A008921 A252181 A251432 * A278675 A114059 A221802

Adjacent sequences: A243203 A243204 A243205 * A243207 A243208 A243209

Keyword

nonn

Author

Alois P. Heinz, Jun 01 2014

Status

approved