OFFSET
0,3
LINKS
Daniel Denton and Peter Doyle, Table of n, a(n) for n = 0..100
Michael Albert, Mike Atkinson, Steve Linton, Permutations generated by stacks and deques, Annals of Combinatorics, 14 (2010) 3-16. (gives method of computation).
Daniel Denton, Methods of computing deque sortable permutations given complete and incomplete information, arXiv:1208.1532.
Stoyan Dimitrov, Sorting by shuffling methods and a queue, arXiv:2103.04332 [math.CO], 2021.
Andrew Elvey-Price and Anthony J. Guttmann, Permutations sortable by deques and by two stacks in parallel, arxiv:1508.02273, 2015
Philippe Flajolet, Bruno Salvy and Paul Zimmermann, Lambda-Upsilon-Omega, The 1989 CookBook, page 105.
Paul Zimmermann, C program for A182216
P. Zimmermann, Introduction to Automatic Analysis, 2012.
EXAMPLE
Up to n=4 all permutations can be sorted by a double-ended queue (deque for short).
For n=5 the permutation 24351 cannot: you first queue 2 on either side, then 4 on either side, then 3 has to be queued on the same side as 4 otherwise it will "block" 2 between 3 and 4, but then whatever side you queue 5, you will block either 2 (between 4 and 5) or 3 (between 4 and 5).
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul Zimmermann, Apr 19 2012
EXTENSIONS
a(13)-a(14) confirmed by Michael Albert, Apr 19 2012
a(16)-a(21) from Michael Albert, Jun 27 2012
a(0)=1 added by N. J. A. Sloane, Sep 12 2012
STATUS
approved