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

Author

Eric W. Weisstein, Jul 12 2017

Keywords

• nonn
• easy

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 (7, -21, 35, -35, 21, -7, 1).

Crossrefs

Cf. A027789 (3-cycles), A289793 (5-cycles), A289794 (6-cycles).

Programs

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]

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.