A241630 Number of compositions of n with exactly five descents.

8, 73, 429, 1945, 7465, 25317, 78068, 222963, 597644, 1518370, 3683950, 8586866, 19320391, 42127208, 89307361, 184578961, 372786467, 737212357, 1429992711, 2724852920, 5107392644, 9427895421, 17157142969, 30810379849, 54643242181, 95783964110, 166059755226

Offset

15,1

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 15..1000

Example

a(15) = 8: [3,2,1,2,1,3,2,1], [3,2,1,3,2,1,2,1], [2,1,3,2,1,3,2,1], [2,1,2,1,3,2,1,2,1], [2,1,3,2,1,2,1,2,1], [3,2,1,2,1,2,1,2,1], [2,1,2,1,2,1,3,2,1], [2,1,2,1,2,1,2,1,2,1].

Maple

b:= proc(n, i) option remember;
      `if`(n=0, 1, convert(series(add(b(n-j, j)*
      `if`(j<i, x, 1), j=1..n), x, 6), polynom))
    end:
a:= n-> coeff(b(n, 0), x, 5):
seq(a(n), n=15..50);

Mathematica

k = 5;
b[n_, i_] := b[n, i] = If[n == 0, 1, Sum[b[n - j, j]*
     If[j < i, x, 1], {j, n}] + O[x]^(k + 1)];
a[n_] := SeriesCoefficient[b[n, 0], {x, 0, k}];
a /@ Range[15, 50] (* Jean-François Alcover, Aug 27 2021, after Maple code *)

Crossrefs

Column k=5 of A238343 and of A238344.

Sequence in context: A058068 A096873 A282786 * A153482 A014991 A015577

Adjacent sequences: A241627 A241628 A241629 * A241631 A241632 A241633

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Apr 26 2014

Status

approved