A294281 Number of ascent sequences of length n with alternating ascents and descents (unaffected by level steps).

1, 1, 2, 4, 9, 22, 59, 172, 547, 1886, 7047, 28360, 122675, 567210, 2796999, 14641044, 81191947, 475148678, 2929442263, 18965690560, 128754649699, 914056305794, 6777666961735, 52367331911180, 421188392986843, 3519168714308702, 30519733808467031

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..550

Formula

a(n) = Sum_{j=0..n} binomial(n-1,j) * A099960(n-j).

Example

a(3) = 4: 000, 001, 010, 011.
a(4) = 9: 0000, 0001, 0010, 0011, 0100, 0101, 0102, 0110, 0111.
a(5) = 22: 00000, 00001, 00010, 00011, 00100, 00101, 00102, 00110, 00111, 01000, 01001, 01002, 01010, 01011, 01020, 01021, 01022, 01100, 01101, 01102, 01110, 01111.

Maple

b:= proc(n, i, t, u) option remember; `if`(n<1, 1, add(
       b(n-1, j, t+`if`(j>i, 1, 0), `if`(i=j, u, 1-u)),
       j=`if`(u=0, i..t+1, 0..i)))
    end:
a:= n-> b(n-1, 0$3):
seq(a(n), n=0..30);

Crossrefs

Cf. A022493, A099960.

Sequence in context: A237770 A187044 A193361 * A293854 A271078 A292790

Adjacent sequences: A294278 A294279 A294280 * A294282 A294283 A294284

Keyword

nonn

Author

Alois P. Heinz, Oct 26 2017

Status

approved