A243229 Number of isoscent sequences of length n with exactly three ascents.

17, 229, 1819, 11172, 58847, 280158, 1242859, 5238042, 21245548, 83685745, 322225735, 1218705577, 4544214608, 16751906196, 61188410692, 221832968059, 799344529621, 2865983103387, 10233713828145, 36419029944617, 129245774064864, 457623216922119

Offset: 6

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 = 6..100

Crossrefs

Column k=3 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, 3):
seq(a(n), n=6..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, 3];
Table[a[n], {n, 6, 35}] (* Jean-François Alcover, Aug 27 2021, after Maple code *)

Formula

G.f.: x^6*(17 - 213*x + 1118*x^2 - 3135*x^3 + 4851*x^4 - 3492*x^5 - 262*x^6 + 1707*x^7 + 82*x^8 - 1050*x^9 + 189*x^10 + 297*x^11 - 122*x^12 + 11*x^13 + 3*x^14) / ((1 - x)^4*(1 - 2*x)^3*(1 - 4*x + 3*x^2 + x^3)^2*(1 - 8*x + 21*x^2 - 18*x^3 - 3*x^4 + 5*x^5 + 3*x^6)) (conjectured). - Colin Barker, May 04 2019