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Search: id:A097976
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| A097976 |
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Sum of largest parts (counted with multiplicity) in all compositions of n. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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G.f.: (1-x)^2*Sum(k*x^k/(1-2*x+x^(k+1))^2, k=1..infinity).
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EXAMPLE
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a(3)=10 because in the compositions111,12,21,3 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.
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MAPLE
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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); (Deutsch)
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CROSSREFS
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Cf. A097940, A092321.
Sequence in context: A107659 A162588 A080615 this_sequence A152548 A090855 A052252
Adjacent sequences: A097973 A097974 A097975 this_sequence A097977 A097978 A097979
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 07 2004
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 28 2005
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