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A008676
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Expansion of 1/(1-x^3 )(1-x^5 ).
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1
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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; refs; listen; history; internal format)
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OFFSET
| 0,16
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COMMENTS
| a(n) gives the number of partitions of n using only the parts 3 and 5. e.g. a(25)=2: 5+5+5+5+5 and 5+5+3+3+3+3+3+3. - Andrew Baxter (baxter(AT)math.rutgers.edu), Jun 20 2011
a(n) gives the 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
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 217
Index to sequences with linear recurrences with constant coefficients, signature (0,0,1,0,1,0,0,-1).
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FORMULA
| G.f.: 1/( (1-x^3) * (1-x^5) )
a(n) = a(n-3) + a(n-5) - a(n-8), a(0)=a(3)=a(5)=a(6)=1, a(1)=a(2)=a(4)=a(6)=a(7)=0.
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MAPLE
| a := proc (n) option remember; if n < 0 then return 0 elif n = 0 then return 1 else return a(n-3)+a(n-5)-a(n-8) end if end proc
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PROG
| (PARI) Vec(O(x^99)+1/(1-x^3)/(1-x^5)) \\ Charles R Greathouse IV, Jun 20 2011
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CROSSREFS
| Cf. A103221.
Sequence in context: A192006 A006928 A087890 * A025893 A025878 A143421
Adjacent sequences: A008673 A008674 A008675 * A008677 A008678 A008679
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Edited by Andrew Baxter (baxter(AT)math.rutgers.edu) - Jun 20, 2011
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