A098132 Number of compositions of n where the smallest part is greater than the number of parts.

0, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 9, 12, 16, 21, 27, 34, 42, 51, 62, 76, 94, 117, 146, 182, 226, 279, 342, 416, 503, 606, 729, 877, 1056, 1273, 1536, 1854, 2237, 2696, 3243, 3891, 4655, 5553, 6607, 7844, 9297, 11006, 13019, 15393, 18195, 21503, 25407, 30010

Offset

1,6

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Hung Viet Chu, Nurettin Irmak, Steven J. Miller, Laszlo Szalay, and Sindy Xin Zhang, Schreier Multisets and the s-step Fibonacci Sequences, arXiv:2304.05409 [math.CO], 2023.

Formula

G.f.: Sum_{n>=0} x^(n*(n+1)) / (1-x)^n.

Example

a(11)=7 because we have: 11, 8+3, 3+8, 7+4, 4+7, 6+5 and 5+6.

Maple

G:=sum(x^(k^2+k)/(1-x)^k, k=0..20): Gser:=series(G, x=0, 67): seq(coeff(Gser, x^n), n=1..65); # Emeric Deutsch, Mar 29 2005

Mathematica

nmax = 60; Rest[CoefficientList[Series[Sum[x^(k*(k+1))/(1-x)^k, {k, 1, Sqrt[nmax] + 1}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 11 2018 *)

Crossrefs

Cf. A003106, A003114, A077229.

Sequence in context: A126327 A328116 A193286 * A017900 A005708 A367637

Adjacent sequences: A098129 A098130 A098131 * A098133 A098134 A098135

Keyword

easy,nonn

Author

Vladeta Jovovic, Sep 27 2004

Extensions

More terms from Emeric Deutsch, Mar 29 2005

Status

approved