A178008 Number of permutations of 1..n with no element e[i>=2]<e[1+floor((i-2)/3)] (3-way heap).

1, 1, 1, 2, 6, 12, 40, 180, 630, 3360, 22680, 113400, 831600, 7484400, 38918880, 302702400, 2918916000, 20432412000, 205837632000, 2500927228800, 21598916976000, 263986763040000, 3837961401120000, 33774060329856000, 431557437548160000, 6658314750743040000

Offset

0,4

Comments

a(n) is also the number of labeled histories for the trifurcating labeled topology that possesses the largest number of labeled histories, among all labeled topologies with 2n+1 leaves. - Noah A Rosenberg, Feb 24 2025

Links

Alois P. Heinz, Table of n, a(n) for n = 0..502

E. H. Dickey, N. A. Rosenberg, Labelled histories with multifurcation and simultaneity, Phil. Trans. R. Soc. B 380 (2025), 20230307.

Wikipedia, D-ary heap

Crossrefs

Simple 2-way heap A056971.

Column k=3 of A273693.

Sequence in context: A094261 A080497 A127724 * A377950 A266005 A056744

Adjacent sequences: A178005 A178006 A178007 * A178009 A178010 A178011

Keyword

nonn,changed

Author

R. H. Hardin, May 17 2010

Extensions

a(0), a(21)-a(25) from Alois P. Heinz, May 27 2016

Status

approved