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A036049 Number of cycles of the permutation created by duality and reversal on the partitions of n. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..50.

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,more,nice

AUTHOR

Olivier Gérard

EXTENSIONS

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

STATUS

approved

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Last modified May 30 18:07 EDT 2020. Contains 334728 sequences. (Running on oeis4.)