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Search: id:A100405
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| A100405 |
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Number of partitions of n where every part appears more than two times. |
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+0
1
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| 0, 0, 1, 1, 1, 2, 1, 2, 3, 3, 3, 7, 5, 6, 11, 10, 10, 17, 15, 20, 26, 25, 29, 44, 41, 47, 63, 67, 72, 99, 97, 114, 143, 148, 168, 216, 216, 248, 306, 328, 358, 443, 462, 527, 629, 665, 739, 898, 936, 1055, 1238, 1330, 1465, 1727, 1837, 2055, 2366, 2543, 2808, 3274
(list; graph; listen)
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OFFSET
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1,6
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FORMULA
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G.f.: Product_{k>0} (1+x^(3*k)/(1-x^k)). More generally, g.f. for number of partitions of n where every part appears more than m times is Product_{k>0} (1+x^((m+1)*k)/(1-x^k)).
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EXAMPLE
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a(6)=2 because we have [2,2,2] and [1,1,1,1,1,1].
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MAPLE
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G:=product((1+x^(3*k)/(1-x^k)), k=1..30): Gser:=series(G, x=0, 80):seq(coeff(Gser, x^n), n=1..70); (Deutsch)
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CROSSREFS
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Cf. A007690.
Sequence in context: A161078 A161294 A161269 this_sequence A081366 A129636 A048219
Adjacent sequences: A100402 A100403 A100404 this_sequence A100406 A100407 A100408
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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), Jan 11 2005
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 06 2005
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