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, 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

Offset

1,2

Links

Eric W. Weisstein, Table of n, a(n) for n = 1..117 (rows n = 1..9, flattened).

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: A109332 A359000 A296542 * A167986 A015727 A034104

Adjacent sequences: A296543 A296544 A296545 * A296547 A296548 A296549

Keyword

nonn,tabf

Author

Eric W. Weisstein, Dec 15 2017

Status

approved