A202062 Number of ascent sequences avoiding the pattern 201.

1, 1, 2, 5, 15, 52, 201, 843, 3764, 17659, 86245, 435492, 2261769, 12033165, 65369590, 361661809, 2033429427, 11597912588, 67004252081, 391599609911, 2312726369640, 13789161819383, 82932744795049, 502777950712812, 3070529443569777, 18879637374473465, 116815588935673706, 727011479685559453

Offset: 0

Author

N. J. A. Sloane, Dec 10 2011

Keywords

• nonn

Comments

It appears that no formula or g.f. is known.

Links

• Andrew Conway and Miles Conway, Table of n, a(n) for n = 0..133
• Giulio Cerbai, Modified ascent sequences and Bell numbers, arXiv:2305.10820 [math.CO], 2023. See p. 27.
• Giulio Cerbai, Anders Claesson and Luca Ferrari, Stack sorting with restricted stacks, arXiv:1907.08142 [cs.DS], 2019.
• Andrew R. Conway, Miles Conway, Andrew Elvey Price and Anthony J. Guttmann, Pattern-avoiding ascent sequences of length 3, arXiv:2111.01279 [math.CO], Nov 01 2021.
• P. Duncan and Einar Steingrimsson, Pattern avoidance in ascent sequences, arXiv preprint arXiv:1109.3641 [math.CO], 2011.
• Anthony Guttmann and Vaclav Kotesovec, L-convex polyominoes and 201-avoiding ascent sequences, arXiv:2109.09928 [math.CO], 2021.

Crossrefs

Total number of ascent sequences is given by A022493.

Number of ascent sequences avoiding 001 (and others) is A000079; 102 is A007051; 101 is A000108; 000 is A202058; 100 is A202059; 110 is A202060; 120 is A202061; 201 is A202062; 210 is A108304; 0123 is A080937; 0021 is A007317.

Formula

Guttmann and Kotesovec give asymptotics: a(n) ~ c * d^n / n^(9/2), where d = (14/3*cos(arccos(13/14)/3) + 8/3) = 7.2958969432397723745722241... is the root of the equation 1 + 5*d - 8*d^2 + d^3 = 0 and c = 35*sqrt((4107 - 84*sqrt(9289) * cos(Pi/3 + arccos(255709*sqrt(9289)/24653006)/3))/Pi)/16 = 13.4299960869439... - Vaclav Kotesovec, Sep 22 2021

Extensions

a(15) from Kanstancin Novikau, Mar 21 2017

a(16)-a(27) from Ildar Gainullin, Feb 11 2020