A228670 Number of permutations of [n] having a shortest ascending run of length 3.

1, 0, 0, 19, 68, 110, 1679, 11941, 59470, 528974, 4907480, 36965659, 370685663, 4086527638, 40650345653, 458464525689, 5857242113368, 72283039099029, 938515852729074, 13416951764772945, 194738851363141390, 2909111655448399908, 46421744844240409407

Offset

3,4

Links

Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 3..480 (first 100 terms from Alois P. Heinz)

Formula

a(n) ~ c * d^n * n!, where d = 0.63140578989563018836245602310621356272419174622597338..., c = 0.2944330707154006599431970237808940992565854768253334... . - Vaclav Kotesovec, Sep 07 2014

Example

a(3) = 1: 123.
a(6) = 19: 124356, 125346, 126345, 134256, 135246, 136245, 145236, 146235, 156234, 234156, 235146, 236145, 245136, 246135, 256134, 345126, 346125, 356124, 456123.

Crossrefs

Column k=3 of A064315.

Sequence in context: A139927 A337197 A357365 * A044157 A044538 A297226

Adjacent sequences: A228667 A228668 A228669 * A228671 A228672 A228673

Keyword

nonn

Author

Alois P. Heinz, Aug 29 2013

Status

approved