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Search: id:A066898
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| A066898 |
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Total number of even parts in all partitions of n. |
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+0
9
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| 0, 1, 1, 4, 5, 11, 15, 28, 38, 62, 85, 131, 177, 258, 346, 489, 648, 890, 1168, 1572, 2042, 2699, 3475, 4532, 5783, 7446, 9430, 12017, 15106, 19073, 23815, 29827, 37011, 46012, 56765, 70116, 86033, 105627, 128962, 157476, 191359, 232499
(list; graph; listen)
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OFFSET
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1,4
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FORMULA
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Sum_{k=1..floor{n/2)} tau(k)*numbpart(n-2*k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 26 2002
a(n)=sum(k*A116482(n,k),k=0..floor(n/2)). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 17 2006
G.f.=sum(x^(2j)/(1-x^(2j)), j=1..infinity)/product((1-x^j), j=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 17 2006
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EXAMPLE
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a(5)=5 because in all the partitions of 5, namely [5], [4,1], [3,2], [3,1,1], [2,2,1], [2,1,1,1], [1,1,1,1,1], we have a total of 0+1+1+0+2+1+0=5 even parts.
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MAPLE
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g:=sum(x^(2*j)/(1-x^(2*j)), j=1..60)/product((1-x^j), j=1..60): gser:=series(g, x=0, 55): seq(coeff(gser, x, n), n=1..50); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 17 2006
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CROSSREFS
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Cf. A000041.
Cf. A000005, A006128, A066897.
Cf. A116482.
Sequence in context: A125577 A053307 A076065 this_sequence A118143 A001350 A077238
Adjacent sequences: A066895 A066896 A066897 this_sequence A066899 A066900 A066901
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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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