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Number of permutations of n elements in which alternating maximal rises and descents are all of length >= 2.
1

%I #39 Apr 24 2018 19:55:38

%S 1,1,0,2,2,14,42,244,1208,7930,52710,405850,3310702,29742388,

%T 285103536,2943395390,32318674810,377660270510,4668433604250,

%U 60946384750028,837286564780496,12079835055678770,182562305754119886,2884622329374990250,47559525570125238782

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

%C 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).

%H Alois P. Heinz, <a href="/A277556/b277556.txt">Table of n, a(n) for n = 0..479</a>

%H Therese Biedl, Ahmad Biniaz, Robert Cummings, Anna Lubiw, Florin Manea, Dirk Nowotka, Jeffrey Shallit, <a href="https://arxiv.org/abs/1801.08565">Rollercoasters and Caterpillars</a>, arXiv:1801.08565 [cs.CG], 2018.

%K nonn

%O 0,4

%A _Jeffrey Shallit_, Nov 16 2016

%E a(0), a(16)-a(24) from _Alois P. Heinz_, Apr 24 2018