A036056 - OEIS

A036056

Sum of the lengths of the cycle types of the permutation created by length sorting on the partitions of n.

1, 1, 1, 3, 3, 7, 11, 20, 25, 37, 54, 74, 98, 131, 169, 227, 293, 380, 486, 622, 787, 970, 1251, 1569, 1946, 2431, 3003, 3713, 4544, 5599, 6831, 8324, 10139, 12305, 14873, 17974, 21632, 26006, 31180, 37334, 44575, 53171, 63257, 75172, 89132, 105523, 124749, 147268, 173520, 204222

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OFFSET

1,4

LINKS

Table of n, a(n) for n=1..50.

PROG

(PARI)

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=vecsort(u, (x, y)->lex(#x, #y), 1+4)); vecsum(Set(OrderCycs(v)))} \\ Andrew Howroyd, Sep 17 2019

CROSSREFS

Cf. A036045-A036056.

Sequence in context: A022403 A082550 A327397 * A339586 A278789 A279829

Adjacent sequences: A036053 A036054 A036055 * A036057 A036058 A036059

KEYWORD

nonn

AUTHOR

Olivier Gérard

EXTENSIONS

a(31)-a(50) from Andrew Howroyd, Sep 17 2019

STATUS

approved