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A102712
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Sum of largest parts of all compositions of n.
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1
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1, 3, 8, 19, 43, 94, 202, 428, 899, 1875, 3890, 8036, 16544, 33962, 69552, 142149, 290017, 590814, 1202016, 2442706, 4958974, 10058216, 20384498, 41282346, 83549603, 168992081, 341627732, 690279026, 1394115072, 2814430326, 5679552630, 11457287926, 23104929222
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 1..1000
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FORMULA
| G.f.: Sum(n*(1-x)^2*x^n/((1-2*x+x^n)*(1-2*x+x^(n+1))), n=1..infinity).
G.f.: (1-x)/(1-2*x)*Sum(x^n/(1-2*x+x^n),n=1..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 28 2008
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EXAMPLE
| a(4) = 19 because we have (4), (3)1, 1(3), (2)2, (2)11, 1(2)1, 11(2) and (1)111; the largest parts, shown between parentheses, add up to 19.
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MAPLE
| G:=sum(n*(1-x)^2*x^n/((1-2*x+x^n)*(1-2*x+x^(n+1))), n=1..45):Gser:=series(G, x=0, 40):seq(coeff(Gser, x^n), n=1..36); (Deutsch)
##
b:= proc(n, m, t) option remember;
`if` (m=1, 1,
`if` (n<m and not t, 0,
`if` (n=0, 1, add (b(n-j, m, j=m or t), j=1..min(n, m)))))
end:
a:= n-> add (m*b(n, m, false), m=1..n):
seq (a(n), n=1..40); # Alois P. Heinz, Oct 21 2011
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CROSSREFS
| Cf. A006128, A097939.
Sequence in context: A065352 A161993 A008466 * A054480 A191787 A121551
Adjacent sequences: A102709 A102710 A102711 * A102713 A102714 A102715
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 05 2005
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 29 2005
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