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A334358 Irregular triangle read by rows: row n gives scaled coefficients of the chromatic polynomial corresponding to colorings of the n-hypercube graph up to automorphism, highest powers first, 0 <= k <= 2^n. 5
1, 0, 1, -1, 0, 1, -2, 3, -2, 0, 1, -12, 72, -256, 579, -812, 644, -216, 0, 1, -32, 496, -4936, 35276, -191840, 820328, -2808636, 7759343, -17276144, 30675244, -42494732, 44214736, -32375904, 14772272, -3125472, 0, 1, -80, 3160, -82080, 1575420, -23805776, 294640000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

The polynomials are scaled by a factor of n!*2^n to ensure integer coefficients. When evaluated at x = k, they give the number of non-isomorphic k-colorings of the n-hypercube graph under the automorphism group of the graph. The size of the automorphism group is n!*2^n. Colors may not be interchanged.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..68 (rows 0..5)

Eric Weisstein's World of Mathematics, Chromatic Polynomial

Eric Weisstein's World of Mathematics, Hypercube Graph

EXAMPLE

Triangle begins:

  0 | 1, 0;

  1 | 1, -1, 0;

  2 | 1, -2, 3, -2, 0;

  3 | 1, -12, 72, -256, 579, -812, 644, -216, 0;

  ...

The corresponding polynomials are:

  x;

  (x^2 - x)/(1!*2^1);

  (x^4 - 2*x^3 + 3*x^2 - 2*x)/(2!*2^2);

  (x^8 - 12*x^7 + 72*x^6 - 256*x^5 + 579*x^4 - 812*x^3 + 644*x^2 - 216*x)/(3!*2^3);

  ...

The polynomial (x^4 - 2*x^3 + 3*x^2 - 2*x)/(2!*2^2) gives A002817 when evaluated at integer values of x.

CROSSREFS

Cf. A002817, A334159, A334248, A334356, A334357.

Sequence in context: A247490 A002120 A021435 * A226556 A007325 A247920

Adjacent sequences:  A334355 A334356 A334357 * A334359 A334360 A334361

KEYWORD

sign,tabf

AUTHOR

Andrew Howroyd, Apr 24 2020

STATUS

approved

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Last modified March 7 19:13 EST 2021. Contains 341928 sequences. (Running on oeis4.)