A289794 Number of 6-cycles in the n-tetrahedral graph.

0, 0, 0, 0, 920, 17760, 122640, 537040, 1794240, 4994640, 12178320, 26840880, 54620280, 104184080, 188348160, 325459680, 541078720, 869994720, 1358615520, 2067768480, 3075954840, 4483100160, 6414845360, 9027424560, 12513177600, 17106746800, 23092009200

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 (9, -36, 84, -126, 126, -84, 36, -9, 1).

Crossrefs

Cf. A027789 (3-cycles), A289792 (4-cycles), A289793 (5-cycles).

Programs

Mathematica

Table[5 Binomial[n, 5] (454 - 409 n + 66 n^2 + n^3), {n, 20}]
LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {0, 0, 0, 0, 920, 17760, 122640, 537040, 1794240}, 20]
CoefficientList[Series[(40 x^4 (-23 - 237 x + 102 x^2 + 116 x^3))/(-1 + x)^9, {x, 0, 20}], x]

Formula

a(n) = 5*binomial(n, 5)*(454 - 409*n + 66*n^2 + n^3).

a(n) = 9*a(n-1)-36*a(n-2)+84*a(n-3)-126*a(n-4)+126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9).

G.f.: (40*x^5*(-23 - 237*x + 102*x^2 + 116*x^3))/(-1 + x)^9.