A317487 Number of 4-cycles in the n-Bruhat graph.

0, 0, 0, 6, 90, 1080, 12600, 151200, 1905120, 25401600, 359251200, 5388768000, 85621536000, 1438441804800, 25499650176000, 475993469952000, 9336794987520000, 192071211171840000, 4135933413900288000, 93058501812756480000, 2184137777840578560000, 53390034569436364800000

Offset

1,4

Links

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

Jennifer Elder, Pamela E. Harris, Jan Kretschmann, and J. Carlos Martínez Mori, Boolean intervals in the weak order of S_n, arXiv:2306.14734 [math.CO], 2023-2024.

Eric Weisstein's World of Mathematics, Bruhat Graph.

Eric Weisstein's World of Mathematics, Graph Cycle.

Formula

a(n) = n!*(n-2)*(n-3)/8 for n > 1. - Andrew Howroyd, Jul 30 2018

From Amiram Eldar, Jun 21 2026: (Start)

Sum_{n>=4} 1/a(n) = 8*(e + gamma - Ei(1))/3 - 32/9, where e = A001113, gamma = A001620 and Ei(1) = A091725.

Sum_{n>=4} (-1)^n/a(n) = 16*(gamma - Ei(-1))/3 - 8/(3*e) - 28/9, where Ei(-1) = -A099285. (End)

Mathematica

a[n_] := n!*(n-2)*(n-3)/8; a[1] = 0; Array[a, 22] (* Amiram Eldar, Jun 21 2026 *)

Prog

(PARI) a(n) = if(n > 1, n!*(n-2)*(n-3)/8, 0); \\ Andrew Howroyd, Jul 30 2018

Crossrefs

Cf. A317486.

Cf. A001113, A001620, A091725, A099285.

Sequence in context: A091800 A336042 A353230 * A397668 A037959 A247150

Adjacent sequences: A317484 A317485 A317486 * A317488 A317489 A317490

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 29 2018

Extensions

Terms a(10) and beyond from Andrew Howroyd, Jul 30 2018

Status

approved