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A317784 Number of ascent sequences of length n avoiding the pattern 0000. 2
1, 1, 2, 5, 14, 47, 180, 773, 3701, 19488, 111890, 695786, 4656185, 33356828, 254675642, 2063984616, 17694054723, 159958176316, 1520689121858, 15165205111010 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

Paul Duncan and Einar Steingrimsson, Pattern avoidance in ascent sequences, arXiv:1109.3641 [math.CO], 2011.

FORMULA

a(n) <= A022493(n) with equality only for n < 4.

MAPLE

b:= proc(n, i, t, p) option remember; `if`(n=0, 1, add(

      `if`(coeff(p, x, j)=3, 0, b(n-1, j, t+

      `if`(j>i, 1, 0), p+x^j)), j=1..t+1))

    end:

a:= n-> b(n, 0$3):

seq(a(n), n=0..12);

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, 3]];

Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 15}] (* Vincenzo Librandi, Feb 12 2020 *)

CROSSREFS

Column k=3 of A294220.

Cf. A022493.

Sequence in context: A287888 A115276 A327702 * A096402 A007268 A326898

Adjacent sequences:  A317781 A317782 A317783 * A317785 A317786 A317787

KEYWORD

nonn,more

AUTHOR

Alois P. Heinz, Aug 06 2018

EXTENSIONS

a(18) from Vaclav Kotesovec, Aug 20 2018

a(19) from Vaclav Kotesovec, Aug 23 2018

STATUS

approved

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Last modified September 30 03:54 EDT 2020. Contains 337434 sequences. (Running on oeis4.)