A243215 Number of 4-matchings of the n X n grid graph.

0, 0, 0, 18, 2593, 39979, 281514, 1301950, 4618099, 13628193, 35115244, 81502564, 174076485, 347418199, 655313518, 1178436234, 2034127639, 3388621645, 5472091824, 8596923568, 13179641449, 19766948739, 29066362930, 41981957974, 59655750843, 83515296889

Offset

0,4

Comments

Number of ways 4 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.: -(6*x^9 -14*x^8 -155*x^7 +474*x^6 +1267*x^5 -7976*x^4 +13539*x^3 +17290*x^2 +2431*x +18)*x^3 / (x-1)^9.

a(n) = (4*n^8 -16*n^7 -60*n^6 +308*n^5 +171*n^4 -1942*n^3 +872*n^2 +3963*n -3366)/6 for n>=4, a(3) = 18, a(n) = 0 for n<=2.

Maple

a:= n-> `if`(n<4, [0$3, 18][n+1], ((((((((4*n-16)*n-60)
       *n+308)*n+171)*n-1942)*n+872)*n+3963)*n-3366)/6):
seq(a(n), n=0..40);

Crossrefs

Column k=4 of A242861.

Sequence in context: A174637 A267065 A356204 * A162449 A318297 A001325

Adjacent sequences: A243212 A243213 A243214 * A243216 A243217 A243218

Keyword

nonn

Author

Alois P. Heinz, Jun 01 2014

Status

approved