A182216 -id:A182216 - cp's OEIS frontend

A215252 Number of indecomposable permutations sortable using two parallel stacks.

0, 1, 1, 3, 12, 56, 289, 1602, 9367, 57075, 359346, 2323416, 15356446, 103389175, 707107627, 4901988047, 34384943850, 243694702311, 1742953208739, 12567593026554, 91280392585747, 667341975412356, 4907899368783645, 36289929612761691, 269660272111724536, 2012845416966620068, 15087243969226496324, 113521159338891300347, 857211201390859034536

Offset: 0

N. J. A. Sloane, Sep 07 2012. a(0)=0 added by N. J. A. Sloane, Sep 12 2012

nonn

Suggested by Peter Doyle in an email message, Sep 04 2012

N. J. A. Sloane, Table of n, a(n) for n = 0..100

Cf. A003319, A216040, A182216, A215257.

INVERTi transform of A216040.

A215257 Number of indecomposable permutations sortable by a double-ended queue.

Original entry on oeis.org

0, 1, 1, 3, 13, 67, 383, 2345, 15069, 100341, 686515, 4797997, 34110765, 245926667, 1793867881, 13214905229, 98177212059, 734746226575, 5534054981071, 41917876423855, 319102504087883, 2440086947417629, 18733909260242195, 144354928765952131, 1116015033661158079, 8654019249571514621, 67292250859412467583, 524583875375437922949

Offset: 0

N. J. A. Sloane, Sep 07 2012. a(0)=0 added by N. J. A. Sloane, Sep 12 2012

nonn

Suggested by Peter Doyle in an email message, Sep 04 2012

N. J. A. Sloane, Table of n, a(n) for n = 0..100

Cf. A003319, A182216, A216040, A215252.

INVERTi transform of A182216.

Name clarified by Peter Doyle, Dec 13 2013

A216040 Number of permutations sortable using two parallel stacks.

Original entry on oeis.org

1, 1, 2, 6, 23, 103, 513, 2760, 15741, 93944, 581303, 3704045, 24180340, 161082639, 1091681427, 7508269793, 52302594344, 368422746908, 2620789110712, 18806093326963, 136000505625886, 990406677136685, 7258100272108212

Offset: 0

Peter Doyle, Aug 30 2012

nonn

			Up to n = 4, the only permutation that can't be sorted is 2341. This fails because after moving 2 to one stack, you must move 3 to the other stack, and now the 4 will block either the 2 or the 3. (If you use a double-ended queue instead of two stacks, then this permutation becomes sortable; cf. A182216.)

Daniel Denton and Peter Doyle, Table of n, a(n) for n = 0..100
Daniel Denton, Methods of computing deque sortable permutations given complete and incomplete information, arXiv:1208.1532 [math.CO], 2012.
Andrew Elvey-Price and Anthony J. Guttmann, Permutations sortable by deques and by two stacks in parallel, arxiv:1508.02273 [math.CO], 2015-2016.
Andrew Elvey-Price and Anthony J. Guttmann, Permutations sortable by deques and by two stacks in parallel, European Journal of Combinatorics, 59 (2017), 71-95.

Cf. A182216, A215252, A215257.

a(0)=1 added by N. J. A. Sloane, Sep 12 2012

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A215252 Number of indecomposable permutations sortable using two parallel stacks.

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A215257 Number of indecomposable permutations sortable by a double-ended queue.

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A216040 Number of permutations sortable using two parallel stacks.

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