A243231 Number of isoscent sequences of length n with exactly five ascents.

53, 2751, 56905, 771451, 8134377, 72508373, 573143602, 4140884203, 27910175578, 178061795837, 1086790574778, 6397136152382, 36542124316824, 203563522508400, 1110216333288652, 5946996009211010, 31369110229193995, 163289639236069520, 840329677373681576

Offset: 9

Author

Joerg Arndt and Alois P. Heinz, Jun 01 2014

Keywords

• nonn

Links

• Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 9..100

Crossrefs

Column k=5 of A242351.

Programs

Maple

b:= proc(n, i, t) option remember; `if`(n<1, 1, expand(add(
      `if`(j>i, x, 1) *b(n-1, j, t+`if`(j=i, 1, 0)), j=0..t+1)))
    end:
a:= n-> coeff(b(n-1, 0$2), x, 5):
seq(a(n), n=9..35);

Mathematica

b[n_, i_, t_] := b[n, i, t] = If[n < 1, 1, Expand[Sum[
    If[j > i, x, 1] *b[n - 1, j, t + If[j == i, 1, 0]], {j, 0, t + 1}]]];
a[n_] := Coefficient[b[n - 1, 0, 0], x, 5];
Table[a[n], {n, 9, 35}] (* Jean-François Alcover, Aug 27 2021, after Maple code *)