A036054 Number of different cycle lengths of the permutation created by length sorting on the partitions of n.

1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 5, 5, 6, 5, 4, 6, 8, 7, 7, 6, 12, 9, 7, 8, 10, 6, 11, 12, 10, 8, 9, 10, 13, 12, 14, 10, 16, 9, 10, 11, 10, 10, 8, 10, 10, 18, 14, 22, 10, 15, 9, 15, 12, 9, 14, 13, 13, 11, 13, 16, 9, 15, 14, 13, 19, 11, 14, 17, 18, 13, 14, 14, 19

Offset

1,4

Links

Table of n, a(n) for n=1..73.

Prog

(PARI)
OrderCycs(v)={my(t=vector(#v), L=List()); for(i=1, #v, my(c=0, j=i); while(!t[j], t[j]=1; j=v[j]; c++); if(c, listput(L, c))); Vec(L)}
a(n)={my(u=vecsort([Vecsmall(Vecrev(p)) | p<-partitions(n)])); my(v=vecsort(u, (x, y)->lex(#x, #y), 1+4)); #Set(OrderCycs(v))} \\ Andrew Howroyd, Sep 17 2019

Crossrefs

Cf. A036045-A036056.

Sequence in context: A234537 A029126 A269850 * A029102 A241086 A194818

Adjacent sequences: A036051 A036052 A036053 * A036055 A036056 A036057

Keyword

nonn

Author

Olivier Gérard

Extensions

a(31)-a(50) from Andrew Howroyd, Sep 17 2019

More terms from Sean A. Irvine, Oct 20 2020

Status

approved