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A098132
Number of compositions of n where the smallest part is greater than the number of parts.
3
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
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.
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
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Sep 27 2004
EXTENSIONS
More terms from Emeric Deutsch, Mar 29 2005
STATUS
approved