A300843 Number of 4-cycles in the n-transposition graph.

0, 0, 9, 162, 2250, 29700, 396900, 5503680, 80015040, 1224720000, 19758816000, 335899872000, 6010631827200, 113048449113600, 2231219390400000, 46134751703040000, 997703235809280000, 22529953070456832000, 530433460332711936000, 13000820106193920000000

Offset

1,3

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Graph Cycle

Eric Weisstein's World of Mathematics, Transposition Graph

Formula

a(n) = 3*n!*(2*binomial(n,3) + binomial(n,4))/4. - Andrew Howroyd, Mar 13 2018

E.g.f.: 3*x^2*(2-x)/(4*(1-x)^5). - Robert Israel, Mar 14 2018

Mathematica

Table[3 n! (2 Binomial[n, 3] + Binomial[n, 4])/4, {n, 25}] (* Vincenzo Librandi, Mar 14 2018 *)
Table[3 (n + 5) Binomial[n, 3] n!/16, {n, 20}] (* Eric W. Weisstein, Mar 14 2018 *)

Prog

(PARI) a(n)={3*n!*(2*binomial(n, 3)+binomial(n, 4))/4} \\ Andrew Howroyd, Mar 13 2018
(Magma) [3*Factorial(n)*(2*Binomial(n, 3)+Binomial(n, 4))/4: n in [1..20]]; // Vincenzo Librandi, Mar 14 2018

Crossrefs

Cf. A300851 (6-cycles), A296528.

Sequence in context: A209962 A084874 A158749 * A133681 A157553 A202438

Adjacent sequences: A300840 A300841 A300842 * A300844 A300845 A300846

Keyword

nonn

Author

Eric W. Weisstein, Mar 13 2018

Extensions

Terms a(9) and beyond from Andrew Howroyd, Mar 13 2018

Status

approved