The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A160254 Expansion of x*(2 - 3*x + x^2 - 4*x^3 + 3*x^4 - 2*x^5 + x*(1 - x - x^3)*sqrt((1 + 2*x)/(1 - 2*x)))/(2*(1 - 3*x + 3*x^2 - 3*x^3 + 4*x^4 - 3*x^5 + 2*x^6)). 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the number of nodes at level n in certain generating tree, denoted C, that embeds the tree of numerical semigroups. Elizalde (2009) established that the number A007323(n) of numerical semigroups of genus n is bounded in C as follows: A000045(n+2) - 1 <= A007323(n) <= a(n) <= 1 + 3*2^(n - 3). LINKS Matthew House, Table of n, a(n) for n = 1..3328 Sergi Elizalde, Improved bounds on the number of numerical semigroups of a given genus, arXiv:0905.0489 [math.CO], May 4, 2009. See Table 1, p. 8. PROG (Maxima) gf : taylor(x*(2 - 3*x + x^2 - 4*x^3 + 3*x^4 - 2*x^5 + x*(1 - x - x^3)*sqrt((1 + 2*x)/(1 - 2*x)))/(2*(1 - 3*x + 3*x^2 - 3*x^3 + 4*x^4 - 3*x^5 + 2*x^6)), x, 0, 100)\$ makelist(ratcoef(gf, x, n), n, 1, 100); /* Franck Maminirina Ramaharo, Jan 15 2019 */ CROSSREFS Cf. A000045, A007323. Sequence in context: A305442 A000073 A255069 * A276661 A005318 A102111 Adjacent sequences: A160251 A160252 A160253 * A160255 A160256 A160257 KEYWORD nonn,easy AUTHOR Jonathan Vos Post, May 06 2009 EXTENSIONS Edited, and name replaced by the g.f. by Franck Maminirina Ramaharo, Jan 15 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 9 23:05 EST 2022. Contains 358710 sequences. (Running on oeis4.)