A036049 - OEIS

A036049

Number of cycles of the permutation created by duality and reversal on the partitions of n.

1, 2, 3, 5, 7, 9, 11, 7, 15, 9, 9, 18, 12, 12, 10, 13, 11, 11, 19, 16, 20, 18, 17, 14, 14, 18, 29, 26, 23, 17, 38, 22, 23, 27, 31, 27, 34, 27, 31, 35, 39, 46, 39, 48, 54, 54, 59, 62, 77, 73, 68, 65, 77, 81, 84, 91, 102, 103, 112, 119, 130, 130, 148, 152, 167

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..65.

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])))); #OrderCycs(v)} \\ Andrew Howroyd, Sep 16 2019

CROSSREFS

Cf. A036045-A036056.

Sequence in context: A075750 A331232 A219050 * A092875 A155498 A069149

Adjacent sequences: A036046 A036047 A036048 * A036050 A036051 A036052

KEYWORD

nonn,nice

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