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%I #12 Oct 21 2020 02:48:49
%S 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,
%T 15,15,15,19,19,22,21,23,27,29,31,31,37,41,41,46,46,55,53,56,60,67,71,
%U 74,83,86,92,101,109,115,121,131,139,151,159,176,184,198
%N Number of different cycle lengths of the permutation created by duality and reversal on the partitions of n.
%o (PARI)
%o 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}
%o 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)}
%o 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
%Y Cf. A036045-A036056.
%K nonn
%O 1,6
%A _Olivier Gérard_
%E a(31)-a(50) from _Andrew Howroyd_, Sep 16 2019
%E More terms from _Sean A. Irvine_, Oct 20 2020
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