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, 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

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