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A320607 Number of parts in all partitions of n in which no part occurs more than four times.

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