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A320611 Number of parts in all partitions of n in which no part occurs more than eight times.

%I A320611 #11 Jul 31 2020 16:42:13
%S A320611 1,3,6,12,20,35,54,86,119,182,254,366,499,697,934,1274,1681,2237,2918,
%T A320611 3830,4927,6377,8128,10388,13120,16600,20796,26076,32419,40318,49798,
%U A320611 61494,75464,92582,112990,137800,167284,202912,245128,295870,355813,427472,511926
%N A320611 Number of parts in all partitions of n in which no part occurs more than eight times.
%H A320611 Alois P. Heinz, <a href="/A320611/b320611.txt">Table of n, a(n) for n = 1..5000</a>
%F A320611 a(n) ~ log(3) * exp(4*Pi*sqrt(n/3)/3) / (Pi * sqrt(2) * 3^(1/4) * n^(1/4)). - _Vaclav Kotesovec_, Oct 18 2018
%p A320611 b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(4*i*(i+1)<n, 0, add(
%p A320611       (l-> [0, l[1]*j]+l)(b(n-i*j, min(n-i*j, i-1))), j=0..min(n/i, 8))))
%p A320611     end:
%p A320611 a:= n-> b(n$2)[2]:
%p A320611 seq(a(n), n=1..50);
%t A320611 Table[Length[Flatten[Select[IntegerPartitions[n], Max[Tally[#][[All, 2]]] <= 8 &]]], {n, 43}] (* _Robert Price_, Jul 31 2020 *)
%Y A320611 Column k=8 of A210485.
%Y A320611 Cf. A104502.
%K A320611 nonn
%O A320611 1,2
%A A320611 _Alois P. Heinz_, Oct 17 2018