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A241626 Number of compositions of n with exactly one descent. 3
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified August 3 05:51 EDT 2020. Contains 336197 sequences. (Running on oeis4.)