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A252778 Number of ways of n-coloring the square grid graph G_(3,3) such that no rectangle exists with sides parallel to the axes having all 4 corners of the same color. 5
0, 0, 156, 14298, 228984, 1821420, 9676020, 39328086, 131914608, 382726584, 991134540, 2342199090, 5133181416, 10561434468, 20593784484, 38341504110, 68569332960, 118371718896, 198054533628, 322265959434, 511426049880, 793510636380, 1206251784276 (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 9 rectangles with sides parallel to the axes.

a(4) = A200045(3,3) = 228984.

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)*(n^7+n^6+n^5-8*n^4-8*n^3+4*n^2+22*n-14).

G.f.: 6 *x^2 *(11*x^7 +92*x^6 +2829*x^5 +13850*x^4 +26045*x^3 +15504*x^2 +2123*x +26) / (x-1)^10.

MAPLE

a:= n-> (((((n^3-9)*n^2+12)*n+18)*n-36)*n+14)*n:

seq(a(n), n=0..30);

CROSSREFS

Cf. A200045, A252779, A252780, A252839.

Sequence in context: A240005 A035838 A035824 * A006112 A239410 A216788

Adjacent sequences:  A252775 A252776 A252777 * A252779 A252780 A252781

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Dec 21 2014

STATUS

approved

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Last modified August 12 23:19 EDT 2020. Contains 336440 sequences. (Running on oeis4.)