A320610 Number of parts in all partitions of n in which no part occurs more than seven times.

1, 3, 6, 12, 20, 35, 54, 78, 119, 173, 245, 347, 480, 657, 894, 1193, 1588, 2097, 2745, 3563, 4612, 5916, 7556, 9609, 12150, 15286, 19177, 23924, 29757, 36876, 45533, 56026, 68758, 84080, 102556, 124735, 151315, 183059, 220998, 266101, 319720, 383306, 458569

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..5000

Formula

a(n) ~ 3^(5/4) * log(2) * exp(Pi*sqrt(7*n/3)/2) / (2^(3/2) * 7^(1/4) * Pi * n^(1/4)). - Vaclav Kotesovec, Oct 18 2018

Maple

b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(7*i*(i+1)/2<n, 0, add(
      (l-> [0, l[1]*j]+l)(b(n-i*j, min(n-i*j, i-1))), j=0..min(n/i, 7))))
    end:
a:= n-> b(n$2)[2]:
seq(a(n), n=1..50);

Mathematica

Table[Length[Flatten[Select[IntegerPartitions[n], Max[Tally[#][[All, 2]]] <= 7 &]]], {n, 43}] (* Robert Price, Jul 31 2020 *)

Crossrefs

Column k=7 of A210485.

Cf. A261775.

Sequence in context: A348464 A182978 A320609 * A320611 A320612 A320613

Adjacent sequences: A320607 A320608 A320609 * A320611 A320612 A320613

Keyword

nonn

Author

Alois P. Heinz, Oct 17 2018

Status

approved