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

Author

Alois P. Heinz, Oct 17 2018

Keywords

• nonn

Links

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

Crossrefs

Column k=7 of A210485.

Cf. A261775.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(7*i*(i+1)/2 [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 *)

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