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%I A320608 #12 Jul 31 2020 16:40:08
%S A320608 1,3,6,12,20,29,47,71,104,150,213,292,405,547,736,977,1292,1688,2198,
%T A320608 2834,3638,4636,5890,7431,9347,11684,14564,18067,22348,27531,33813,
%U A320608 41378,50504,61438,74561,90208,108896,131096,157485,188717,225682,269285,320691
%N A320608 Number of parts in all partitions of n in which no part occurs more than five times.
%H A320608 Alois P. Heinz, <a href="/A320608/b320608.txt">Table of n, a(n) for n = 1..5000</a>
%F A320608 a(n) ~ log(6) * exp(Pi*sqrt(5*n)/3) / (2 * Pi * 5^(1/4) * n^(1/4)). - _Vaclav Kotesovec_, Oct 18 2018
%p A320608 b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(5*i*(i+1)/2<n, 0, add(
%p A320608       (l-> [0, l[1]*j]+l)(b(n-i*j, min(n-i*j, i-1))), j=0..min(n/i, 5))))
%p A320608     end:
%p A320608 a:= n-> b(n$2)[2]:
%p A320608 seq(a(n), n=1..50);
%t A320608 Table[Length[Flatten[Select[IntegerPartitions[n], Max[Tally[#][[All, 2]]] <= 5 &]]], {n, 43}] (* _Robert Price_, Jul 31 2020 *)
%Y A320608 Column k=5 of A210485.
%Y A320608 Cf. A219601.
%K A320608 nonn
%O A320608 1,2
%A A320608 _Alois P. Heinz_, Oct 17 2018

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