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A036048
Number of different cycle lengths of the permutation created by duality and reversal on the partitions of n.
1
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
OFFSET
1,6
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
KEYWORD
nonn
EXTENSIONS
a(31)-a(50) from Andrew Howroyd, Sep 16 2019
More terms from Sean A. Irvine, Oct 20 2020
STATUS
approved