The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A335712 The sum of the sizes of the minimal fixed points over all compositions of n. 3
 1, 1, 2, 6, 12, 27, 54, 115, 237, 486, 997, 2030, 4122, 8350, 16881, 34054, 68609, 138052, 277500, 557328, 1118546, 2243589, 4498004, 9014053, 18058159, 36166338, 72415886, 144970116, 290170091, 580721926, 1162077483, 2325206168, 4652155420, 9307199819 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 REFERENCES M. Archibald, A. Blecher and A. Knopfmacher, Fixed points in compositions and words, accepted by the Journal of Integer Sequences. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..500 M. Archibald, A. Blecher, and A. Knopfmacher, Fixed Points in Compositions and Words, J. Int. Seq., Vol. 23 (2020), Article 20.11.1. FORMULA G.f.: Sum_{j>=1} (Product_{i=1..j-1} (x/(1-x)-x^i)) j x^j (1-x)/(1-2x). EXAMPLE Example: For n=3 the a(3)=2 values are the first 1s in 111 and 12 (the other compositions 21 and 3 do not have any fixed points). PROG (PARI) my(N=44, x='x+O('x^N)); Vec( sum(j=1, N, prod(i=1, j-1, (x/(1-x)-x^i) ) *j*x^j * (1-x)/(1-2*x) ) ) \\ Joerg Arndt, Jun 18 2020 CROSSREFS Cf. A099036, A335713, A335714. Sequence in context: A029863 A091919 A059078 * A166963 A188476 A155583 Adjacent sequences:  A335709 A335710 A335711 * A335713 A335714 A335715 KEYWORD nonn AUTHOR Margaret Archibald, Jun 18 2020 EXTENSIONS a(21)-a(34) from Alois P. Heinz, Jun 18 2020 STATUS approved

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

Last modified August 2 02:53 EDT 2021. Contains 346409 sequences. (Running on oeis4.)