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
KEYWORD
nonn
AUTHOR
Margaret Archibald, Jun 18 2020
EXTENSIONS
a(21)-a(34) from Alois P. Heinz, Jun 18 2020
STATUS
approved