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A334358
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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.
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5
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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
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OFFSET
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0,7
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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sign,tabf
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AUTHOR
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STATUS
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approved
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