A097941 Total number of smallest parts in all compositions of n.

1, 3, 6, 15, 31, 72, 155, 340, 738, 1595, 3424, 7335, 15642, 33243, 70432, 148808, 313571, 659188, 1382682, 2894369, 6047397, 12613209, 26265098, 54610722, 113387831, 235117449, 486933645, 1007290340, 2081469759, 4296789924, 8861401891, 18258651137, 37589337434

Offset: 1

Author

Vladeta Jovovic, Sep 05 2004

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 500 terms from Vincenzo Librandi)
• Knopfmacher, Arnold; Munagi, Augustine O. Smallest parts in compositions, Kotsireas, Ilias S. (ed.) et al., Advances in combinatorics. In part based on the 3rd Waterloo workshop on computer algebra (WWCA, W80) 2011, Waterloo, Canada, May 26-29, 2011. Berlin: Springer. 197-207 (2013).

Crossrefs

Cf. A092269, A097939, A097940, A238342.

Programs

Mathematica

Drop[ CoefficientList[ Series[(1 - x)^2*Sum[x^k/(1 - x - x^k)^2, {k, 50}], {x, 0, 30}], x], 1] (* Robert G. Wilson v, Sep 08 2004 *)

Formula

G.f.: (1-x)^2 * Sum_{k>=1} x^k/(1-x-x^k)^2.

a(n) ~ n*2^(n-3). - Vaclav Kotesovec, Apr 30 2014

a(n) = Sum_{k=0..n} k * A238342(n,k). - Alois P. Heinz, Oct 15 2024

Extensions

More terms from Robert G. Wilson v, Sep 08 2004