A241628 Number of compositions of n with exactly three descents.

3, 18, 78, 264, 786, 2097, 5179, 11998, 26400, 55593, 112814, 221639, 423318, 788518, 1436302, 2564135, 4494967, 7750068, 13160903, 22039386, 36434095, 59514365, 96139570, 153699716, 243345157, 381779187, 593848668, 916277405, 1403004758, 2132797015

Offset

9,1

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 9..1000

Example

a(9) = 3: [2,1,3,2,1], [3,2,1,2,1], [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, 4), polynom))
    end:
a:= n-> coeff(b(n, 0), x, 3):
seq(a(n), n=9..50);

Mathematica

k = 3;
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[9, 50] (* Jean-François Alcover, Aug 27 2021, after Maple code *)

Crossrefs

Column k=3 of A238343 and of A238344.

Sequence in context: A094033 A245580 A043008 * A056319 A056310 A309259

Adjacent sequences: A241625 A241626 A241627 * A241629 A241630 A241631

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Apr 26 2014

Status

approved