A357242 Number of n node tournaments that have exactly two circular triads.

24, 240, 2240, 21840, 228480, 2580480, 31449600, 412473600, 5801241600, 87178291200, 1394852659200, 23683435776000, 425430061056000, 8062248370176000, 160770717499392000, 3365514444644352000, 73798027581358080000, 1691677863018823680000, 40464026199993876480000

Offset

4,1

Links

Table of n, a(n) for n=4..22.

Ian R. Harris and Ryan P. A. McShane, Counting Tournaments with a Specified Number of Circular Triads, Journal of Integer Sequences, Vol. 27 (2024), Article 24.8.7. See pages 2, 23.

J. B. Kadane, Some equivalence classes in paired comparisons, The Annals of Mathematical Statistics, 37 (1966), 488-494.

Formula

a(n) = n!*(n - 3 + (1/18)*(n - 4)*(n - 5)) (proven by Kadane).

Example

For n = 4 the a(4) = 24 solution is 4!*(4 - 3 + (1/18)*(4 - 4)*(4 - 5)) = 24.

Prog

(R) fact(n)*(n-3+(1/18)*(n-4)*(n-5))

Crossrefs

Sequence in context: A353119 A052520 A052724 * A000536 A151720 A052652

Adjacent sequences: A357239 A357240 A357241 * A357243 A357244 A357245

Keyword

nonn,easy

Author

Ian R Harris, Sep 19 2022

Status

approved