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

Author

Margaret Archibald, Jun 18 2020

Keywords

• nonn
• easy

Examples

			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).
		

References

• M. Archibald, A. Blecher and A. Knopfmacher, Fixed points in compositions and words, accepted by the Journal of Integer Sequences.

Links

• 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, A335712, A335713.

Programs

PARI

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

Formula

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

Extensions

More terms from Michel Marcus, Jun 18 2020