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

Author

Ian R Harris, Sep 19 2022

Keywords

• nonn
• easy

Examples

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

Links

• 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.

Programs

R

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

Formula

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