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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. 4
0, 0, 144, 13932, 226224, 1809360, 9637200, 39225564, 131679072, 382238784, 990202320, 2340528300, 5130339984, 10556808912, 20586528144, 38330476380, 68553028800, 118348187904, 198021287952, 322219869804, 511363229040, 793426309200, 1206140143824 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 27 12:48 EDT 2022. Contains 354896 sequences. (Running on oeis4.)