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A357257 Number of n-node tournaments that have exactly three circular triads. 2
240, 2880, 33600, 403200, 5093760, 68275200, 972787200, 14724864000, 236396160000, 4016659046400, 72067387392000, 1362306097152000, 27071765360640000, 564357385912320000, 12317692759916544000, 280955128203509760000 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,1

LINKS

Table of n, a(n) for n=5..20.

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

FORMULA

a(n) = n!*(2*(n-4) + (1/3)*(n-5)*(n-6) + (1/162)*(n-6)*(n-7)*(n-8)*[n>5]) (see Kadane).

E.g.f.: (x^4 - 18*x^3 + 72*x^2 - 108*x + 54)*x^5/((3^3)*(1-x)^4).

EXAMPLE

a(6) = 6!*(2*(6-4) + (1/3)*(6-5)*(6-6) + (1/162)*(6-6)*(6-7)*(6-8)*[6>5]) = 2880.

MATHEMATICA

Table[n!*(2*(n-4) + (1/3)*(n-5)*(n-6) + (1/162)*(n-6)*(n-7)*(n-8)*Boole[n>5]), {n, 5, 20}] (* Stefano Spezia, Sep 27 2022 *)

CROSSREFS

Cf. A357242, A357248, A357266.

Sequence in context: A004009 A269033 A180277 * A005950 A279746 A004536

Adjacent sequences: A357253 A357254 A357255 * A357258 A357259 A357260

KEYWORD

nonn

AUTHOR

Ian R Harris, Ryan P. A. McShane, Sep 20 2022

STATUS

approved

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Last modified November 30 18:07 EST 2022. Contains 358453 sequences. (Running on oeis4.)