A289792 Number of 4-cycles in the n-tetrahedral graph.

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

Offset

1,5

Comments

Extended to a(1)-a(5) using the formula.

Links

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).

Formula

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.

Mathematica

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]

Crossrefs

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

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 12 2017

Status

approved