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

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..400

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).

Formula

G.f.: (1-x)^2*Sum(k*x^k/(1-x-x^k)^2, k=1..infinity).

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

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 *)

Crossrefs

Cf. A046746, A092309.

Sequence in context: A097164 A133628 A280486 * A032280 A300158 A156303

Adjacent sequences: A097937 A097938 A097939 * A097941 A097942 A097943

Keyword

easy,nonn

Author

Vladeta Jovovic, Sep 05 2004

Extensions

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

Status

approved