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A342073
Number of n-colorings of the vertices of the 5-dimensional cross polytope such that no two adjacent vertices have the same color.
4
0, 0, 0, 0, 0, 120, 4320, 78120, 913920, 7575120, 46751040, 224587440, 881591040, 2946869640, 8659691040, 22915652760, 55611279360, 125508233760, 266320172160, 535945217760, 1030028705280, 1901347885080, 3386866301280, 5844714201480, 9803816225280
OFFSET
0,6
LINKS
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
FORMULA
a(n) = -205056*n + 593016*n^2 - 698250*n^3 + 448015*n^4 - 175004*n^5 + 43608*n^6 - 6990*n^7 + 700*n^8 - 40*n^9 + n^10.
a(n) = (n - 4)*(n - 3)*(n - 2)*(n - 1)*n*(-8544 + 6909*n - 2240*n^2 + 365*n^3 - 30*n^4 + n^5).
a(n) = Sum_{i=1..10} A334279(5,i)*n^i.
From Chai Wah Wu, Jan 19 2024: (Start)
a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n > 10.
G.f.: x^5*(-2170680*x^5 - 1145400*x^4 - 272400*x^3 - 37200*x^2 - 3000*x - 120)/(x - 1)^11. (End)
MATHEMATICA
p = ChromaticPolynomial[CompleteGraph[Table[2, 5]], x];
Table[p /. x -> n, {n, 0, 50}]
CROSSREFS
Analogous for k-dimensional cross polytope: A091940 (k=2), A115400 (k=3), A334281 (k=4), A342074 (k=6), A342075 (k=7)
Sequence in context: A166596 A000514 A179060 * A055360 A001807 A111155
KEYWORD
nonn
AUTHOR
Peter Kagey, Feb 27 2021
STATUS
approved