A241629 Number of compositions of n with exactly four descents.

5, 37, 189, 751, 2558, 7762, 21577, 55867, 136478, 317416, 707817, 1521755, 3168262, 6410970, 12646075, 24378923, 46028497, 85269218, 155238256, 278130152, 490983234, 854910432, 1469679627, 2496560526, 4193815403, 6971437570, 11474937414, 18712755604

Offset

12,1

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 12..1000

Example

a(12) = 5: [3,2,1,3,2,1], [2,1,2,1,3,2,1], [2,1,3,2,1,2,1], [3,2,1,2,1,2,1], [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, 5), polynom))
    end:
a:= n-> coeff(b(n, 0), x, 4):
seq(a(n), n=12..50);

Mathematica

k = 4;
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[12, 50] (* Jean-François Alcover, Aug 27 2021, after Maple code *)

Crossrefs

Column k=4 of A238343 and of A238344.

Sequence in context: A270326 A269815 A270931 * A273539 A095924 A270019

Adjacent sequences: A241626 A241627 A241628 * A241630 A241631 A241632

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Apr 26 2014

Status

approved