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Search: id:A005308
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| A005308 |
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Bosonic string states.
(Formerly M0310)
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+0
1
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| 1, 0, 0, 0, 1, 1, 2, 2, 4, 4, 7, 8, 14, 16, 25, 31, 47, 58, 85, 107, 153, 195, 271, 348, 480, 616, 834, 1077, 1445, 1863, 2478, 3194, 4216, 5431, 7118, 9157, 11942, 15329, 19884, 25485, 32916, 42090, 54147, 69093, 88563, 112769, 144056, 183028, 233112, 295525
(list; graph; listen)
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OFFSET
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1,7
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COMMENT
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See the reference for precise definition.
The g.f. -(z+1)*(z**7+z**6+z**5-z**4-z**3+z**2-z+1)/(-1+z**5+3*z**4); conjectured by S. Plouffe in his 1992 dissertation is wrong.
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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).
T. Curtright, ``Counting symmetry patterns in the spectra of strings,'' in H. J. de Vega and N. S\'{a}nchez, editors, String Theory, Quantum Cosmology and Quantum Gravity. Integrable and Conformal Invariant Theories. World Scientific, Singapore, 1987, pp. 304-333.
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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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G.f.: Product (1 - x^k)^{-c(k)}; c(k) = 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, ....
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CROSSREFS
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Sequence in context: A026929 A035554 A032278 this_sequence A151532 A056503 A055636
Adjacent sequences: A005305 A005306 A005307 this_sequence A005309 A005310 A005311
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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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