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Search: id:A160254
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| A160254 |
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Arising from lower and upper bounds on the number of numerical semigroups of genus n. |
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1
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| 1, 2, 4, 7, 13, 24, 44, 81, 151, 280, 525, 984, 1859, 3511, 6682, 12709, 24334, 46565, 89626, 172381, 333262, 643733, 1249147, 2421592, 4713715, 9165792, 17888456, 34873456, 68212220, 133269997, 261167821, 511211652, 1003436520, 1967293902
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OFFSET
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1,2
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COMMENT
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From Table 1, p.8 of Elizalde. A000045(n-2) = F(n-2) <= A007323(n) <= a(n) <= 1+3*(2^(n-3))). Abstract: We improve the previously best known lower and upper bounds on the number n_g of numerical semigroups of genus g. Starting from a known recursive description of the tree T of numerical semigroups, we analyze some of its properties and use them to construct approximations of T by generating trees whose nodes are labeled by certain parameters of the semigroups. We then translate the succession rules of these trees into functional equations for the generating functions that enumerate their nodes, and solve these equations to obtain the bounds. Some of our bounds involve the Fibonacci numbers, and the others are expressed as generating functions. We also give upper bounds on the number of numerical semigroups having an infinite number of descendants in T.
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LINKS
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Sergi Elizalde, Improved bounds on the number of numerical semigroups of a given genus, May 4, 2009.
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CROSSREFS
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Cf. A000045, A007323.
Sequence in context: A006744 A054175 A000073 this_sequence A005318 A102111 A059633
Adjacent sequences: A160251 A160252 A160253 this_sequence A160255 A160256 A160257
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KEYWORD
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nonn,uned
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), May 06 2009
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