A241626 Number of compositions of n with exactly one descent.

1, 3, 9, 19, 41, 77, 142, 247, 421, 689, 1113, 1750, 2712, 4128, 6208, 9201, 13502, 19585, 28158, 40109, 56689, 79486, 110703, 153129, 210536, 287752, 391172, 528961, 711837, 953429, 1271421, 1688293, 2232899, 2941798, 3861621, 5051174, 6584958, 8556655

Offset

3,2

Links

Joerg Arndt, Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 3..4000 (first 1000 terms from Joerg Arndt and Alois P. Heinz)

Example

a(3) = 1: [2,1].
a(4) = 3: [3,1], [1,2,1], [2,1,1].
a(5) = 9: [3,2], [4,1], [2,1,2], [3,1,1], [1,3,1], [2,2,1], [2,1,1,1], [1,1,2,1], [1,2,1,1].

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

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, Normal[Series[Sum[b[n - j, j]* If[j < i, x, 1], {j, 1, n}], {x, 0, 2}]]]; a[n_] := Coefficient[b[n, 0], x, 1]; Table[a[n], {n, 3, 50}] (* Jean-François Alcover, Feb 06 2015, after Maple *)

Crossrefs

Column k=1 of A238343 and of A238344.

Sequence in context: A208972 A307541 A268403 * A160704 A279673 A146662

Adjacent sequences: A241623 A241624 A241625 * A241627 A241628 A241629

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Apr 26 2014

Status

approved