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Search: id:A092130
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| A092130 |
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Number of partitions of n into distinct parts == 1 mod 3, with 1 as the smallest part. |
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| 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 2, 1, 1, 3, 1, 1, 3, 2, 1, 4, 3, 1, 4, 4, 2, 5, 5, 2, 5, 7, 3, 6, 8, 4, 6, 10, 6, 7, 12, 7, 8
(list; graph; listen)
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OFFSET
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1,18
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COMMENT
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Also number of partitions of n such that if k is the largest part, then k occurs exactly once and integers from 1 to k-1 occur a positive multiple of 3 times. Example: a(18)=2 because we have [3,2,2,2,1,1,1,1,1,1,1,1,1] and [3,2,2,2,2,2,2,1,1,1]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 18 2006
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FORMULA
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G.f.=x*product(1+x^(1+3k), k=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 18 2006
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EXAMPLE
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For a(24), we have 19+4+1, 16+7+1, 13+10+1, so a(24)=3.
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MAPLE
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g:=x*product(1+x^(1+3*k), k=1..25): gser:=series(g, x=0, 70): seq(coeff(gser, x, n), n=1..51); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 18 2006
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PROGRAM
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(PARI) for(i=0, 50, print1(", "polcoeff(prod(k=1, 50, (1+x^(3*k+1))), i)))
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CROSSREFS
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Cf. A027349.
Adjacent sequences: A092127 A092128 A092129 this_sequence A092131 A092132 A092133
Sequence in context: A127242 A025853 A025847 this_sequence A029298 A059835 A093998
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KEYWORD
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nonn
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Mar 30 2004
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