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A202059 Number of ascent sequences avoiding the pattern 100. 5

%I #38 Jan 19 2024 21:14:48

%S 1,1,2,5,14,44,153,583,2410,10721,50965,257393,1374187,7722862,

%T 45520064,280502924,1802060232,12040040899,83475921469,599400745354,

%U 4449689901306,34096169966924,269286884243138,2189193150557825,18297258191472880,157049750065028868

%N Number of ascent sequences avoiding the pattern 100.

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

%H Andrew Conway and Miles Conway, <a href="/A202059/b202059.txt">Table of n, a(n) for n = 0..628</a>

%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, 2011

%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

%O 0,3

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

%E Corrected a(7), was 383, but should be 583 according to Duncan-Steimgrimsson paper and independent computation. - _Andrew Baxter_, Jan 06 2014

%E a(0) and a(15)-a(21) from _Alois P. Heinz_, Jan 06 2014

%E a(22) from _Alois P. Heinz_, Oct 06 2014

%E a(23) from _Alois P. Heinz_, Apr 20 2016

%E More terms from _Anthony Guttmann_, Nov 04 2021

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)