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A182517 Chromatic invariant of the square grid graph G_(n,n). 1
1, 1, 3, 72, 11423, 11187798, 65460885384, 2247082682913972, 447548280314975144427, 513427482871084962707467332 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The square grid graph G_(n,n) has n^2 = A000290(n) vertices and 2*n*(n-1) = A046092(n-1) edges. The chromatic invariant equals the absolute value of the first derivative of the chromatic polynomial evaluated at 1.

LINKS

Table of n, a(n) for n=1..10.

Eric Weisstein's World of Mathematics, Chromatic Invariant

Eric Weisstein's World of Mathematics, Grid Graph

Wikipedia, Chromatic Polynomial

FORMULA

a(n) = |(d/dq P(n,q))_{q=1}| with P(n,q) = Sum_{k=0..n^2} A182368(n,k) * q^(n^2-k).

MATHEMATICA

Abs[Table[Derivative[1][ChromaticPolynomial[GridGraph[{n, n}]]][1], {n, 7}]] (* Eric W. Weisstein, May 01 2017 *)

CROSSREFS

Cf. A000290, A046092, A182368 (chromatic polynomial).

Sequence in context: A202948 A213986 A156908 * A135866 A307925 A006270

Adjacent sequences:  A182514 A182515 A182516 * A182518 A182519 A182520

KEYWORD

nonn,more

AUTHOR

Alois P. Heinz, May 03 2012

EXTENSIONS

a(10) from Andrew Howroyd, Apr 23 2018

STATUS

approved

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Last modified September 18 16:42 EDT 2020. Contains 337170 sequences. (Running on oeis4.)