%I #42 May 24 2023 13:10:21

%S 1,1,2,5,15,52,201,843,3764,17659,86245,435492,2261769,12033165,

%T 65369590,361661809,2033429427,11597912588,67004252081,391599609911,

%U 2312726369640,13789161819383,82932744795049,502777950712812,3070529443569777,18879637374473465,116815588935673706,727011479685559453

%N Number of ascent sequences avoiding the pattern 201.

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

%H Andrew Conway and Miles Conway, <a href="/A202062/b202062.txt">Table of n, a(n) for n = 0..133</a>

%H Giulio Cerbai, <a href="https://arxiv.org/abs/2305.10820">Modified ascent sequences and Bell numbers</a>, arXiv:2305.10820 [math.CO], 2023. See p. 27.

%H Giulio Cerbai, Anders Claesson and Luca Ferrari, <a href="https://arxiv.org/abs/1907.08142">Stack sorting with restricted stacks</a>, arXiv:1907.08142 [cs.DS], 2019.

%H Andrew R. Conway, Miles Conway, Andrew Elvey Price and Anthony J. Guttmann, <a href="https://arxiv.org/abs/2111.01279">Pattern-avoiding ascent sequences of length 3</a>, arXiv:2111.01279 [math.CO], Nov 01 2021.

%H P. Duncan and Einar Steingrimsson, <a href="http://arxiv.org/abs/1109.3641">Pattern avoidance in ascent sequences</a>, arXiv preprint arXiv:1109.3641 [math.CO], 2011.

%H Anthony Guttmann and Vaclav Kotesovec, <a href="https://arxiv.org/abs/2109.09928">L-convex polyominoes and 201-avoiding ascent sequences</a>, arXiv:2109.09928 [math.CO], 2021.

%F 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

%Y 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.

%K nonn,more

%O 0,3

%A _N. J. A. Sloane_, Dec 10 2011

%E a(15) from _Kanstancin Novikau_, Mar 21 2017

%E a(16)-a(27) from _Ildar Gainullin_, Feb 11 2020