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A289794 Number of 6-cycles in the n-tetrahedral graph. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 22 23:20 EDT 2021. Contains 348181 sequences. (Running on oeis4.)