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A289792
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Number of 4-cycles in the n-tetrahedral graph.
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4
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0, 0, 0, 0, 90, 540, 1995, 5775, 14280, 31500, 63630, 119790, 212850, 360360, 585585, 918645, 1397760, 2070600, 2995740, 4244220, 5901210, 8067780, 10862775, 14424795, 18914280, 24515700, 31439850, 39926250, 50245650, 62702640, 77638365, 95433345, 116510400
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OFFSET
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1,5
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COMMENTS
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Extended to a(1)-a(5) using the formula.
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LINKS
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Table of n, a(n) for n=1..33.
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 (7, -21, 35, -35, 21, -7, 1).
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FORMULA
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a(n) = binomial(n - 1, 4) * (210 - 41*n + 7*n^2)/2.
a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7).
G.f.: (-15*x^5*(6 - 6*x + 7*x^2))/(-1 + x)^7.
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MATHEMATICA
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Table[Binomial[n - 1, 4] (210 - 41 n + 7 n^2)/2, {n, 20}]
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 0, 0, 90, 540, 1995}, 20]
CoefficientList[Series[-((15 x^4 (6 - 6 x + 7 x^2))/(-1 + x)^7), {x, 0, 20}], x]
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CROSSREFS
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Cf. A027789 (3-cycles), A289793 (5-cycles), A289794 (6-cycles).
Sequence in context: A203734 A066116 A233638 * A156738 A211446 A203787
Adjacent sequences: A289789 A289790 A289791 * A289793 A289794 A289795
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KEYWORD
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nonn,easy
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AUTHOR
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Eric W. Weisstein, Jul 12 2017
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STATUS
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approved
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