A243237 Number of isoscent sequences of length n with maximal number of ascents.

1, 1, 1, 4, 3, 25, 17, 2, 172, 53, 7, 1422, 436, 72, 5, 7894, 1854, 271, 19, 86372, 19919, 3179, 312, 14, 527951, 102503, 14324, 1287, 56, 7237537, 1373018, 198783, 20572, 1350, 42, 48862041, 8055893, 1032239, 96532, 5866, 174, 801902467, 129068117, 16767855

Offset

0,4

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 0..100

Formula

a(n) = A242351(n,n+3-ceiling(2*sqrt(n+2))).

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-> (p-> coeff(p, x, degree(p)))(b(n-1, 0$2)):
seq(a(n), n=0..50);

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_] := With[{p = b[n - 1, 0, 0]}, Coefficient[p, x, Exponent[p, x]]];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Aug 27 2021, after Maple code *)

Crossrefs

Sequence in context: A286328 A189742 A350173 * A072044 A286795 A127138

Adjacent sequences: A243234 A243235 A243236 * A243238 A243239 A243240

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 01 2014

Status

approved