A252779 Number of ways of n-coloring the square grid graph G_(3,3) such that no rectangle exists having all 4 corners of the same color.

0, 0, 144, 13932, 226224, 1809360, 9637200, 39225564, 131679072, 382238784, 990202320, 2340528300, 5130339984, 10556808912, 20586528144, 38330476380, 68553028800, 118348187904, 198021287952, 322219869804, 511363229040, 793426309200, 1206140143824

Offset

0,3

Comments

The square grid graph G_(3,3) has 9 vertices, 12 edges and 10 rectangles.

Links

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

Eric Weisstein's World of Mathematics, Grid Graph

Formula

a(n) = n*(n-1)^2*(n^6+2*n^5+3*n^4-6*n^3-15*n^2-4*n+12).

G.f.: 36 *x^2 *(x^7 +18*x^6 +481*x^5 +2280*x^4 +4355*x^3 +2594*x^2 +347*x+4) / (x-1)^10.

Maple

a:= n-> (((((n^3-10)*n^2+20)*n+5)*n-28)*n+12)*n:
seq(a(n), n=0..30);

Crossrefs

Cf. A252778, A252780, A252839.

Sequence in context: A231697 A238932 A230969 * A238284 A249181 A352511

Adjacent sequences: A252776 A252777 A252778 * A252780 A252781 A252782

Keyword

nonn,easy

Author

Alois P. Heinz, Dec 21 2014

Status

approved