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%I #12 May 18 2020 20:21:16
%S 1,3,6,12,15,29,41,65,91,132,179,257,339,465,616,823,1062,1402,1790,
%T 2320,2939,3750,4701,5946,7398,9243,11428,14161,17368,21372,26056,
%U 31823,38596,46838,56499,68208,81868,98292,117489,140390,167068,198796,235655,279239
%N Number of parts in all partitions of n in which no part occurs more than four times.
%H Alois P. Heinz, <a href="/A320607/b320607.txt">Table of n, a(n) for n = 1..5000</a>
%F a(n) ~ 3^(1/4) * log(5) * exp(2*Pi*sqrt(2*n/15)) / (2^(5/4) * 5^(1/4) * Pi * n^(1/4)). - _Vaclav Kotesovec_, Oct 18 2018
%p b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(2*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, 4))))
%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]]]<5&]]],{n,50}] (* _Harvey P. Dale_, May 18 2020 *)
%Y Column k=4 of A210485.
%Y Cf. A035959.
%K nonn
%O 1,2
%A _Alois P. Heinz_, Oct 17 2018
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