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

Author

Alois P. Heinz, Jun 01 2014

Keywords

• nonn

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

Crossrefs

Column k=4 of A242861.

Programs

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);

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.