A097976 Sum of largest parts (counted with multiplicity) in all compositions of n.
1, 4, 10, 24, 53, 118, 253, 542, 1143, 2396, 4986, 10330, 21304, 43808, 89837, 183838, 375514, 765880, 1559979, 3173794, 6450514, 13098246, 26574968, 53877266, 109153818, 221002456, 447199458, 904420716, 1828192748, 3693782678, 7459897213, 15059812760, 30390898331
Offset: 1
Examples
a(3)=10 because in the compositions 111, 12, 21, 3 the largest parts are 1, 2, 2, 3 with multiplicities 3, 1, 1, 1, respectively and 3*1 + 1*2 + 1*2 + 1*3 = 10.
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..1000
Programs
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Maple
G:=(1-x)^2*sum(k*x^k/(1-2*x+x^(k+1))^2, k=1..45): Gser:=series(G,x=0,40): seq(coeff(Gser,x^n),n=1..35); # Emeric Deutsch, Jul 28 2005
Formula
G.f.: (1-x)^2 * Sum_{k>=1} k*x^k/(1 - 2*x + x^(k+1))^2.
Extensions
More terms from Emeric Deutsch, Jul 28 2005