A320612 - OEIS

%I #11 Jul 31 2020 16:42:37

%S 1,3,6,12,20,35,54,86,128,182,264,376,520,718,978,1318,1761,2338,3070,

%T 4008,5206,6707,8604,10982,13933,17604,22155,27745,34627,43061,53338,

%U 65859,81074,99458,121687,148469,180633,219202,265386,320473,386147,464245,556925

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

%H Alois P. Heinz, <a href="/A320612/b320612.txt">Table of n, a(n) for n = 1..5000</a>

%F a(n) ~ log(10) * exp(Pi*sqrt(3*n/5)) / (2 * Pi * 15^(1/4) * n^(1/4)). - _Vaclav Kotesovec_, Oct 18 2018

%p b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(9*i*(i+1)/2<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, 9))))

%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]]] <= 9 &]]], {n, 43}] (* _Robert Price_, Jul 31 2020 *)

%Y Column k=9 of A210485.

%Y Cf. A261776.

%K nonn

%O 1,2

%A _Alois P. Heinz_, Oct 17 2018