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A342074
Number of n-colorings of the vertices of the 6-dimensional cross polytope such that no two adjacent vertices have the same color.
4
0, 0, 0, 0, 0, 0, 720, 35280, 866880, 13849920, 158004000, 1347524640, 8866186560, 46496324160, 201705744240, 748737990000, 2444976293760, 7178449299840, 19276199691840, 47983899216960, 111920569776000, 246727594270080, 517702915311120, 1039979954779920
OFFSET
0,7
LINKS
Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
FORMULA
a(n) = -22852200*n + 70164670*n^2 - 89812001*n^3 + 64407806*n^4 - 29113410*n^5 + 8790285*n^6 - 1822164*n^7 + 260868*n^8 - 25405*n^9 + 1610*n^10 - 60*n^11 + n^12.
a(n) = (n - 5)*(n - 4)*(n - 3)*(n - 2)*(n - 1)*n*(190435 - 149879*n + 49144*n^2 - 8605*n^3 + 850*n^4 - 45*n^5 + n^6).
a(n) = Sum_{i=1..12} A334279(6,i)*n^i.
From Chai Wah Wu, Jan 19 2024: (Start)
a(n) = 13*a(n-1) - 78*a(n-2) + 286*a(n-3) - 715*a(n-4) + 1287*a(n-5) - 1716*a(n-6) + 1716*a(n-7) - 1287*a(n-8) + 715*a(n-9) - 286*a(n-10) + 78*a(n-11) - 13*a(n-12) + a(n-13) for n > 12.
G.f.: x^6*(-287250480*x^6 - 150137280*x^5 - 35996400*x^4 - 5126400*x^3 - 464400*x^2 - 25920*x - 720)/(x - 1)^13. (End)
MATHEMATICA
p = ChromaticPolynomial[CompleteGraph[Table[2, 6]], x];
Table[p /. x -> n, {n, 0, 50}]
CROSSREFS
Analogous for k-dimensional cross polytope: A091940 (k=2), A115400 (k=3), A334281 (k=4), A342073 (k=5), A342075 (k=7).
Sequence in context: A166759 A181504 A179061 * A055361 A092716 A246194
KEYWORD
nonn
AUTHOR
Peter Kagey, Feb 27 2021
STATUS
approved