%I #12 Jul 31 2020 16:40:19

%S 1,3,6,12,20,35,47,78,111,165,228,330,444,614,820,1108,1452,1930,2491,

%T 3255,4175,5366,6802,8665,10880,13705,17089,21336,26401,32716,40207,

%U 49458,60452,73863,89780,109101,131902,159415,191864,230741,276470,331021,394970

%N Number of parts in all partitions of n in which no part occurs more than six times.

%H Alois P. Heinz, <a href="/A320609/b320609.txt">Table of n, a(n) for n = 1..5000</a>

%F a(n) ~ log(7) * exp(2*Pi*sqrt(n/7)) / (2 * Pi * 7^(1/4) * n^(1/4)). - _Vaclav Kotesovec_, Oct 18 2018

%p b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(3*i*(i+1)<n, 0, add(

%p (l-> [0, l[1]*j]+l)(b(n-i*j, min(n-i*j, i-1))), j=0..min(n/i, 6))))

%p end:

%p a:= n-> b(n$2)[2]:

%p seq(a(n), n=1..50);

%t Table[Length[Flatten[Select[IntegerPartitions[n], Max[Tally[#][[All, 2]]] <= 6 &]]], {n, 43}] (* _Robert Price_, Jul 31 2020 *)

%Y Column k=6 of A210485.

%Y Cf. A035985.

%K nonn

%O 1,2

%A _Alois P. Heinz_, Oct 17 2018