A182517 Chromatic invariant of the square grid graph G_(n,n).

1, 1, 3, 72, 11423, 11187798, 65460885384, 2247082682913972, 447548280314975144427, 513427482871084962707467332

Offset: 1

Author

Alois P. Heinz, May 03 2012

Keywords

• nonn
• more

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
• Wikipedia, Chromatic Polynomial

Crossrefs

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

Programs

Mathematica

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

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).

Extensions

a(10) from Andrew Howroyd, Apr 23 2018