A335713 The sum of the sizes of the largest fixed points over all compositions of n.

1, 1, 3, 7, 16, 34, 73, 155, 324, 674, 1393, 2861, 5852, 11929, 24239, 49127, 99360, 200598, 404377, 814135, 1637363, 3290067, 6605980, 13255451, 26583994, 53290694, 106787166, 213919062, 428415074, 857794856, 1717201360, 3437092882, 6878672565, 13764822699

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} (x/(1-x))^(j-1) j x^j Sum_{k>=j} Product_{i=j+1..k} (x/(1-x) - x^i).

Example

For n=3 the a(3)=3 values are the first 1 in the composition 111 and the 2 in the composition 12 (the compositions 21 and 3 do not have any fixed points).

Crossrefs

Cf. A099036, A335712, A335714.

Sequence in context: A178455 A281811 A238089 * A026734 A026767 A240740

Adjacent sequences: A335710 A335711 A335712 * A335714 A335715 A335716

Keyword

nonn

Author

Margaret Archibald, Jun 18 2020

Extensions

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

Status

approved