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Search: id:A008616
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| A008616 |
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Expansion of 1/((1-x^2)(1-x^5)). |
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+0
3
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| 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 5, 4, 5, 4, 5, 5, 5, 5, 5, 5, 6, 5, 6, 5, 6, 6, 6, 6, 6, 6, 7, 6, 7, 6, 7, 7, 7, 7, 7, 7, 8, 7, 8, 7, 8, 8, 8, 8, 8, 8, 9, 8, 9, 8, 9, 9, 9, 9, 9, 9, 10, 9, 10, 9, 10, 10, 10, 10, 10, 10
(list; graph; listen)
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OFFSET
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0,11
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COMMENT
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Number of partitions of n into parts of size two and five.
It appears that, for n>=2, a(n-2) is also (1) the number of partitions of 3n that are 6-term arithmetic progressions and (2) Floor[n/2]-Floor[2n/5]. [From John W. Layman (layman(AT)math.vt.edu), Jun 29 2009]
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REFERENCES
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D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 100.
G. E. Andrews, K. Eriksson, Integer Partitions, Cambridge Univ. Press, 2004. page 30 Exer. 48
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LINKS
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Index entries for two-way infinite sequences
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 213
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FORMULA
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G.f.: 1/((1-x^2)(1-x^5)).
Euler transform of finite sequence [0, 1, 0, 0, 1].
a(n) = -a(-7-n) = a(n-10)+1 = a(n-2)+a(n-5)-a(n-7). - Michael Somos Jan 25 2005
a(n)=7/20+n/10+(-1)^n/4+(A105384(n)+2*( A010891(n)+A105384(n+4)))/5. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 28 2009]
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PROGRAM
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(PARI) a(n)=polcoeff(1/((1-x^2)*(1-x^5))+x*O(x^n), n)
(PARI) {a(n)=if(n<-6, -a(-7-n), polcoeff( 1/(1-x^2)/(1-x^5)+x*O(x^n), n))} /* Michael Somos Jan 25 2005 */
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CROSSREFS
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A000217(a(n))=A0025810(n).
A008615 [From John W. Layman (layman(AT)math.vt.edu), Jun 29 2009]
Sequence in context: A083023 A084359 A143935 this_sequence A097471 A025868 A050252
Adjacent sequences: A008613 A008614 A008615 this_sequence A008617 A008618 A008619
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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