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

1,5

Comments

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

Links

Table of n, a(n) for n=1..27.

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).

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.

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]

Crossrefs

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

Sequence in context: A083142 A332191 A068163 * A235881 A051984 A232732

Adjacent sequences: A289791 A289792 A289793 * A289795 A289796 A289797

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 12 2017

Status

approved