

A335714


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


2



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
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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.


FORMULA

G.f.: x*(1x)^3/((12*x)*(1xx^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*(1x)^3)/((12*x)*(1xx^2)^2) + O(x^40)) \\ Michel Marcus, Jun 18 2020


CROSSREFS

Cf. A099036, A335712, A335713.
Sequence in context: A129362 A301981 A083579 * A215112 A265108 A328184
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



