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Search: id:A001973
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| A001973 |
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Expansion of (1+x^3 )/(1-x)(1- x^2 )^2 (1-x^3 ).
(Formerly M2441 N0969)
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+0
2
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| 1, 1, 3, 5, 8, 12, 18, 24, 33, 43, 55, 69, 86, 104, 126, 150, 177, 207, 241, 277, 318, 362, 410, 462, 519, 579, 645, 715, 790, 870, 956, 1046, 1143, 1245, 1353, 1467, 1588, 1714, 1848, 1988
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Contribution from Weisenhorn Paul (paulweisenhorn(AT)online.de), Jun 01 2009: (Start)
a(1..3)=0; a(n)is the number of partitions of 2*(n+1) with 4 different
numbers from the set {1,..,n}; the number of partitions of 2*n+2-C and
2*n+2+C are equal; example: n=6; 2*n+2=14; a(6)=3;(10,1),(11,1),(12,2),
(13,2),(14,3),(15,2),(16,2),(17,1),(18,1);
(End)
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
A. Cayley, Numerical tables supplementary to second memoir on quantics, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 2, p. 276-281.
M. Jeger,Einfuehrung in die Kombinatorik,Klett,1975,pages 110- [From Weisenhorn Paul (paulweisenhorn(AT)online.de), Jun 01 2009]
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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Contribution from Weisenhorn Paul (paulweisenhorn(AT)online.de), Jun 01 2009: (Start)
a(n) is the coefficient of x^(2*n+2) from the GF.
product[s=1..4] (x^s-x^(n+1))/(1-x^s);
(End)
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MAPLE
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A001973:=(1-z+z**2)/(z+1)/(z**2+z+1)/(z-1)**4; [Conjectured by S. Plouffe in his 1992 dissertation.]
with(combstruct):ZL:=[st, {st=Prod(left, right), left=Set(U, card=r+1), right=Set(U, card<r), U=Sequence(Z, card>=2)}, unlabeled]: subs(r=2, stack): seq(count(subs(r=2, ZL), size=m), m=6..45) ; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 07 2008
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CROSSREFS
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Sequence in context: A167385 A098202 A164653 this_sequence A020745 A004398 A055606
Adjacent sequences: A001970 A001971 A001972 this_sequence A001974 A001975 A001976
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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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