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.
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