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

Author

Vladeta Jovovic, Sep 27 2004

Keywords

• easy
• nonn

Examples

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

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
• Hùng Việt Chu, Nurettin Irmak, Steven J. Miller, László Szalay, and Sindy Xin Zhang, Schreier Multisets and the s-step Fibonacci Sequences, arXiv:2304.05409 [math.CO], 2023. See also Integers (2024) Vol. 24A, Art. No. A7, p. 4.

Crossrefs

Cf. A003106, A003114, A077229.

Programs

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 *)

Formula

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

Extensions

More terms from Emeric Deutsch, Mar 29 2005