A243217 Number of 5-matchings of the n X n grid graph.

0, 0, 0, 0, 3388, 157000, 2135356, 15836664, 81324796, 325679904, 1088989348, 3174085648, 8301786980, 19888285976, 44304931948, 92833927816, 184597383660, 350812701616, 640815379476, 1130391980512, 1933082192404, 3215240556392, 5215796556572, 8271817286296

Offset: 0

Author

Alois P. Heinz, Jun 01 2014

Keywords

• nonn

Comments

Number of ways 5 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=5 of A242861.

Programs

Maple

a:= n-> `if`(n<5, [0$4, 3388][n+1], ((((((((((4*n-20)*n-100)*n+640)
    *n+635)*n-7589)*n+2370)*n+39275)*n-35789)*n-74246)*n+86580)/15):
seq(a(n), n=0..40);

Formula

G.f.: 4*(2*x^11 -6*x^10 +17*x^9 -559*x^8 +3298*x^7 -5840*x^6 -8668*x^5 +55222*x^4 -105932*x^3 -148674*x^2 -29933*x -847)*x^4 / (x-1)^11.

a(n) = (4*n^10 -20*n^9 -100*n^8 +640*n^7 +635*n^6 -7589*n^5 +2370*n^4 +39275*n^3 -35789*n^2 -74246*n +86580)/15 for n>=5, a(4) = 3388, a(n) = 0 for n<=3.