A335714 The sum of the sizes (positions) of fixed points over all compositions of n.

1, 1, 4, 8, 19, 41, 89, 189, 398, 830, 1719, 3539, 7251, 14797, 30096, 61044, 123531, 249501, 503117, 1013165, 2037986, 4095546, 8223919, 16502823, 33097639, 66349021, 132954724, 266337584, 533388643, 1067965265, 2137907009, 4279099869, 8563658486, 17136379382

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

Table of n, a(n) for n=1..34.

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.: x*(1-x)^3/((1-2*x)*(1-x-x^2)^2).

Example

For n=3 the a(3)=4 values are the first 1 in the composition 111 and both values in the composition 12 (the compositions 21 and 3 have no fixed points).

Prog

(PARI) Vec((x*(1-x)^3)/((1-2*x)*(1-x-x^2)^2) + O(x^40)) \\ Michel Marcus, Jun 18 2020

Crossrefs

Cf. A099036, A335712, A335713.

Sequence in context: A129362 A301981 A083579 * A215112 A340948 A265108

Adjacent sequences: A335711 A335712 A335713 * A335715 A335716 A335717

Keyword

nonn,easy

Author

Margaret Archibald, Jun 18 2020

Extensions

More terms from Michel Marcus, Jun 18 2020

Status

approved