A308631 Related to the position of the smallest part in all compositions of n.

1, 2, 7, 15, 36, 80, 174, 371, 787, 1644, 3410, 7031, 14423, 29455, 59948, 121656, 246302, 497661, 1003864, 2022143, 4068597, 8178131, 16425116, 32965907, 66125958, 132577442, 265700195, 532313023, 1066152092

Offset

3,2

Links

Table of n, a(n) for n=3..31.

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), V'(z,1,1).

Formula

G.f.: (x-1)^2*sum_{j>=1} x^(2*j+1)/((1-x-x^j)*(1-x-x^(j+1))^2).

Maple

(z-1)^2*add(z^(2*j+1)/(1-z-z^j)/(z^(j+1)+z-1)^2, j=1..34) ;
taylor(%, z=0, 32) ;
gfun[seriestolist](%) ;

Crossrefs

Sequence in context: A216633 A295145 A151998 * A052130 A366130 A368675

Adjacent sequences: A308628 A308629 A308630 * A308632 A308633 A308634

Keyword

nonn,easy

Author

R. J. Mathar, Jun 12 2019

Status

approved