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

Author

Joerg Arndt and Alois P. Heinz, Apr 26 2014

Keywords

• nonn

Examples

			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].
		

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)

Crossrefs

Column k=1 of A238343 and of A238344.

Programs

Maple

b:= proc(n, i) option remember;
      `if`(n=0, 1, convert(series(add(b(n-j, j)*
      `if`(j 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 *)