A202058 Number of ascent sequences avoiding the pattern 000.

1, 1, 2, 4, 10, 27, 83, 277, 1015, 4007, 17047, 77451, 374889, 1923168, 10427250, 59544957, 357236992, 2245822801, 14762969601, 101264286082, 723499803180, 5375063821727, 41459660565329, 331546282841906, 2745163969235517, 23505333233440927, 207895424692608432

Offset

0,3

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..176

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, 2011

Mathematica

b[n_, i_, t_, p_, k_] := b[n, i, t, p, k] = If[n==0, 1, Sum[If[Coefficient[ p, x, j]==k, 0, b[n-1, j, t + If[j>i, 1, 0], p+x^j, k]], {j, 1, t+1}]];
a[n_] := b[n, 0, 0, 0, Min[n, 2]];
Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 17}] (* Jean-François Alcover, Sep 01 2018, after Alois P. Heinz in A294220 *)

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; 0000 is A317784.

Column k=2 of A294220.

Sequence in context: A138356 A287693 A275428 * A346999 A148107 A148108

Adjacent sequences: A202055 A202056 A202057 * A202059 A202060 A202061

Keyword

nonn

Author

N. J. A. Sloane, Dec 10 2011

Extensions

a(15)-a(17) from Alois P. Heinz, Nov 09 2012

a(18)-a(20) from Giovanni Resta, Jan 06 2014

a(21) from Vaclav Kotesovec, Aug 21 2018

a(22) from Vaclav Kotesovec, Aug 22 2018

More terms from Anthony Guttmann, Nov 04 2021

Status

approved