A036048 - OEIS

A036048

Number of different cycle lengths of the permutation created by duality and reversal on the partitions of n.

1, 1, 1, 1, 1, 2, 3, 2, 3, 2, 2, 6, 4, 4, 3, 5, 4, 4, 6, 8, 8, 7, 8, 8, 8, 9, 13, 13, 10, 10, 15, 15, 15, 15, 19, 19, 22, 21, 23, 27, 29, 31, 31, 37, 41, 41, 46, 46, 55, 53, 56, 60, 67, 71, 74, 83, 86, 92, 101, 109, 115, 121, 131, 139, 151, 159, 176, 184, 198

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OFFSET

1,6

LINKS

Table of n, a(n) for n=1..69.

PROG

(PARI)

Dual(v)={my(u=vectorsmall(v[1]), k=0); forstep(i=#u, 1, -1, while(k<#v&&v[k+1]>=i, k++); u[i]=k); u}

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=vector(#u, i, vecsearch(u, Dual(u[#u+1-i])))); #Set(OrderCycs(v))} \\ Andrew Howroyd, Sep 16 2019

CROSSREFS

Cf. A036045-A036056.

Sequence in context: A371442 A175066 A066102 * A145384 A339601 A117666

Adjacent sequences: A036045 A036046 A036047 * A036049 A036050 A036051

KEYWORD

nonn

AUTHOR

Olivier Gérard

EXTENSIONS

a(31)-a(50) from Andrew Howroyd, Sep 16 2019

More terms from Sean A. Irvine, Oct 20 2020

STATUS

approved