A097940 Sum of smallest parts (counted with multiplicity) of all compositions of n.

1, 4, 8, 20, 37, 86, 173, 372, 788, 1680, 3550, 7554, 15994, 33820, 71374, 150376, 316151, 663474, 1389760, 2906116, 6066899, 12645608, 26318870, 54700044, 113536171, 235363832, 487342781, 1007969620, 2082597193, 4298660754, 8864505305, 18263797648, 37597869188

Offset: 1

Author

Vladeta Jovovic, Sep 05 2004

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A046746, A092309.

Programs

Mathematica

Drop[ CoefficientList[ Series[(1 - x)^2*Sum[k*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} k*x^k/(1-x-x^k)^2.

a(n) ~ n * 2^(n-3). - Vaclav Kotesovec, Sep 05 2014

a(n) = Sum_{k=1..n} A308630(n,k). - R. J. Mathar, Jun 12 2019

Extensions

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