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A342075
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Number of n-colorings of the vertices of the 7-dimensional cross polytope such that no two adjacent vertices have the same color.
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4
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0, 0, 0, 0, 0, 0, 0, 5040, 322560, 10342080, 216518400, 3261535200, 37026823680, 325474269120, 2264594492160, 12789814237200, 60389186457600, 245221330273920, 877374833287680, 2821277454690240, 8284633867238400, 22503569636419200, 57135310310453760
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OFFSET
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0,8
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LINKS
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Peter Kagey, Table of n, a(n) for n = 0..1000
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FORMULA
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a(n) = -3597143040*n + 11590795728*n^2 - 15837356724*n^3 + 12355698460*n^4 - 6212542175*n^5 + 2144307578*n^6 - 526197678*n^7 + 93450369*n^8 - 12064836*n^9 + 1122618*n^10 - 73423*n^11 + 3206*n^12 - 84*n^13 + n^14.
a(n) = (n - 6)*(n - 5)*(n - 4)*(n - 3)*(n - 2)*(n - 1)*n*(n^7 - 63 n^6 + 1708 n^5 - 25795 n^4 + 234094 n^3 - 1275281 n^2 + 3858049 n - 4996032).
a(n) = Sum_{i=1..14} A334279(7,i)*n^i.
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MATHEMATICA
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p = ChromaticPolynomial[CompleteGraph[Table[2, 7]], x];
Table[p /. x -> n, {n, 0, 50}]
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CROSSREFS
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Analogous for k-dimensional cross polytope: A091940 (k=2), A115400 (k=3), A334281 (k=4), A342073 (k=5), A342074 (k=6).
Cf. A334279, A342088.
Sequence in context: A228910 A258419 A179062 * A055362 A246195 A246615
Adjacent sequences: A342072 A342073 A342074 * A342076 A342077 A342078
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KEYWORD
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nonn
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AUTHOR
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Peter Kagey, Feb 27 2021
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STATUS
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approved
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