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A036050 Sum of the lengths of the cycle types of the permutation created by duality and reversal on the partitions of n. 1
1, 1, 1, 1, 1, 3, 6, 17, 10, 35, 49, 53, 91, 125, 169, 220, 290, 378, 394, 507, 709, 917, 1229, 1475, 1924, 2347, 2851, 3293, 3568, 5597, 6739, 8130, 10131, 12250, 14401, 17705, 21569, 25967, 31174, 37186, 44462, 52964, 63187, 74504, 88467, 105179, 124120, 147040, 172031, 202775 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

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

CROSSREFS

Cf. A036045-A036056.

Sequence in context: A301515 A014645 A195996 * A173877 A101525 A139476

Adjacent sequences:  A036047 A036048 A036049 * A036051 A036052 A036053

KEYWORD

nonn

AUTHOR

Olivier Gérard

EXTENSIONS

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

STATUS

approved

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Last modified November 27 07:28 EST 2021. Contains 349365 sequences. (Running on oeis4.)