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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
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
Eric Weisstein's World of Mathematics, Chromatic Invariant
Eric Weisstein's World of Mathematics, Grid Graph
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
KEYWORD
nonn,more
AUTHOR
Alois P. Heinz, May 03 2012
EXTENSIONS
a(10) from Andrew Howroyd, Apr 23 2018
STATUS
approved