A277556 Number of permutations of n elements in which alternating maximal rises and descents are all of length >= 2.

1, 1, 0, 2, 2, 14, 42, 244, 1208, 7930, 52710, 405850, 3310702, 29742388, 285103536, 2943395390, 32318674810, 377660270510, 4668433604250, 60946384750028, 837286564780496, 12079835055678770, 182562305754119886, 2884622329374990250, 47559525570125238782

Offset

0,4

Comments

A length-t rise in a permutation a() is a list of t+1 consecutive values a(i), ..., a(i+t) for which a(i) < a(i+1) < ... < a(i+t), and similarly for a descent. By "maximal" we mean it can't be increased in length on either side. For example, 3 4 5 2 1 6 7 8 has a rise of length 2 (3,4,5), followed by a descent of length 2 (5,2,1), followed by a rise of length 3 (1,6,7,8).

Links

Alois P. Heinz, Table of n, a(n) for n = 0..479

Therese Biedl, Ahmad Biniaz, Robert Cummings, Anna Lubiw, Florin Manea, Dirk Nowotka, Jeffrey Shallit, Rollercoasters and Caterpillars, arXiv:1801.08565 [cs.CG], 2018.

Crossrefs

Sequence in context: A226157 A264508 A194689 * A321179 A345370 A166114

Adjacent sequences: A277553 A277554 A277555 * A277557 A277558 A277559

Keyword

nonn

Author

Jeffrey Shallit, Nov 16 2016

Extensions

a(0), a(16)-a(24) from Alois P. Heinz, Apr 24 2018

Status

approved