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Search: id:A008676
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| A008676 |
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Expansion of 1/(1-x^3 )(1-x^5 ). |
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+0
2
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| 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 5, 4, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5
(list; graph; listen)
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OFFSET
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0,16
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COMMENT
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a(n) gives number of partitions of n+8 involving both a 3 and a 5. e.g. a(25)=2 and we may write 33 as 5+5+5+5+5+5+3 and 5+5+5+3+3+3+3+3+3. 11*3 doesn't count as no 5 is involved. - Jon Perry (perry(AT)globalnet.co.uk), Jul 03 2004
Conjecture. a(n) = Floor[2*(n + 3)/3] - Floor[3*(n + 3)/5]. [From John W. Layman (layman(AT)math.vt.edu), Sep 23 2009]
Also, it appears that a(n) gives the number of distinct multisets of n-1 integers, each of which is -2, +3, or +4, such that the sum of the members of each multiset is 2. E.g., for n=5, the multiset {-2,-2,3,3}, and no others, of n-1=4 members, sums to 2, so a(5)=1. [From John W. Layman (layman(AT)math.vt.edu), Sep 23 2009]
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 217
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CROSSREFS
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Sequence in context: A086412 A006928 A087890 this_sequence A025893 A025878 A143421
Adjacent sequences: A008673 A008674 A008675 this_sequence A008677 A008678 A008679
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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