A335712 The sum of the sizes of the minimal fixed points over all compositions of n.

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

Offset: 1

Author

Margaret Archibald, Jun 18 2020

Keywords

• nonn

Examples

			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).
		

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.

Crossrefs

Cf. A099036, A335713, A335714.

Programs

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

Formula

G.f.: Sum_{j>=1} (Product_{i=1..j-1} (x/(1-x)-x^i)) j x^j (1-x)/(1-2x).

Extensions

a(21)-a(34) from Alois P. Heinz, Jun 18 2020