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A289793
Number of 5-cycles in the n-tetrahedral graph.
4
0, 0, 0, 0, 312, 3024, 14868, 51744, 145152, 350784, 759528, 1511136, 2810808, 4948944, 8324316, 13470912, 21088704, 32078592, 47581776, 69023808, 98163576, 137147472, 188568996, 255534048, 341732160, 451513920, 589974840, 763045920, 977591160, 1241512272
OFFSET
1,5
COMMENTS
Extended to a(1)-a(5) using the formula.
LINKS
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Tetrahedral Graph
Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1).
FORMULA
a(n) = 6*binomial(n, 5)*(-78 + 21*n + n^2).
a(n) = 8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)-28*a(n-6)+8*a(n-7)-a(n-8).
G.f.: (-12*x^5*(-26 - 44*x + 49*x^2))/(-1 + x)^8.
MATHEMATICA
Table[6 Binomial[n, 5] (-78 + 21 n + n^2), {n, 20}]
LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 0, 0, 0, 312, 3024, 14868, 51744}, 20]
CoefficientList[Series[-((12 x^4 (-26 - 44 x + 49 x^2))/(-1 + x)^8), {x, 0, 20}], x]
CROSSREFS
Cf. A027789 (3-cycles), A289792 (4-cycles), A289794 (6-cycles).
Sequence in context: A270608 A233939 A233934 * A364992 A022044 A156403
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jul 12 2017
STATUS
approved