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Search: id:A066897
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| A066897 |
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Total number of odd parts in all partitions of n. |
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+0
10
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| 1, 2, 5, 8, 15, 24, 39, 58, 90, 130, 190, 268, 379, 522, 722, 974, 1317, 1754, 2330, 3058, 4010, 5200, 6731, 8642, 11068, 14076, 17864, 22528, 28347, 35490, 44320, 55100, 68355, 84450, 104111, 127898, 156779, 191574, 233625, 284070, 344745
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OFFSET
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1,2
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FORMULA
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Sum_{k=1..n} b(k)*numbpart(n-k), where b(k)=A001227(k)=number of odd divisors of k. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 26 2002
a(n)=sum(k*A103919(n,k),k=0..n). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 13 2006
G.f.=sum(x^(2j-1)/(1-x^(2j-1)), j=1..infinity)/product(1-x^j, j=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 13 2006
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EXAMPLE
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a(4)=8 because in the partitions of 4, namely [4],[3,1],[2,2],[2,1,1],[1,1,1,1], we have a total of 0+2+0+2+4=8 odd parts.
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MAPLE
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g:=sum(x^(2*j-1)/(1-x^(2*j-1)), j=1..70)/product(1-x^j, j=1..70): gser:=series(g, x=0, 45): seq(coeff(gser, x^n), n=1..44); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 13 2006
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CROSSREFS
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Cf. A000041.
Cf. A001227, A006128, A066898.
Cf. A103919.
Sequence in context: A121641 A058884 A073335 this_sequence A078697 A066629 A154327
Adjacent sequences: A066894 A066895 A066896 this_sequence A066898 A066899 A066900
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KEYWORD
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easy,nonn
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AUTHOR
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Naohiro Nomoto (n_nomoto(AT)yabumi.com), Jan 24 2002
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 26 2002
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