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A296546 Triangle read by rows T(n,k): number of undirected cycles of length k in the complete tripartite graph K_n,n,n (n = 1...; k = 3..3n) 1
1, 8, 15, 24, 16, 27, 108, 324, 774, 1620, 2268, 1584, 64, 396, 1728, 7200, 27648, 87480, 232704, 476928, 663552, 463104, 125, 1050, 6000, 35800, 198000, 977400, 4392000, 17068320, 56376000, 151632000, 311040000, 430272000, 299289600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..35.

Eric Weisstein's World of Mathematics, Cycle Polynomial

Eric Weisstein's World of Mathematics, Complete Tripartite Graph

FORMULA

Row sums of T(n,k) give A234616(n).

EXAMPLE

Written as cycle polynomials:

x^3

8 x^3 + 15 x^4 + 24 x^5 + 16 x^6

27 x^3 + 108 x^4 + 324 x^5 + 774 x^6 + 1620 x^7 + 2268 x^8 + 1584 x^9

64 x^3 + 396 x^4 + 1728 x^5 + 7200 x^6 + 27648 x^7 + 87480 x^8 + 232704 x^9 + 476928 x^10 + 663552 x^11 + 463104 x^12

giving the array

1

8, 15, 24, 16

27, 108, 324, 774, 1620, 2268, 1584

64, 396, 1728, 7200, 27648, 87480, 232704, 476928, 663552, 463104

MATHEMATICA

Table[Tally[Length /@ FindCycle[CompleteGraph[{n, n, n}], Infinity, All]][[All, 2]], {n, 4}] // Flatten

CROSSREFS

Cf. A234616 (number of undirected cycles in K_n,n,n).

Cf. A144151 (cycle polynomial coefficients of complete graph K_n).

Cf. A291909 (cycle polynomial coefficients of complete bipartite graph K_n,n).

Sequence in context: A126622 A109332 A296542 * A167986 A015727 A034104

Adjacent sequences:  A296543 A296544 A296545 * A296547 A296548 A296549

KEYWORD

nonn,tabf

AUTHOR

Eric W. Weisstein, Dec 15 2017

STATUS

approved

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Last modified February 25 14:07 EST 2021. Contains 341609 sequences. (Running on oeis4.)