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A036049
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Number of cycles of the permutation created by duality and reversal on the partitions of n.
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1
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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, 68, 65, 77, 81, 84, 91, 102, 103, 112, 119, 130, 130, 148, 152, 167
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OFFSET
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1,2
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LINKS
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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