A320610 - OEIS

%I #11 Jul 31 2020 16:41:26

%S 1,3,6,12,20,35,54,78,119,173,245,347,480,657,894,1193,1588,2097,2745,

%T 3563,4612,5916,7556,9609,12150,15286,19177,23924,29757,36876,45533,

%U 56026,68758,84080,102556,124735,151315,183059,220998,266101,319720,383306,458569

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

%H Alois P. Heinz, <a href="/A320610/b320610.txt">Table of n, a(n) for n = 1..5000</a>

%F a(n) ~ 3^(5/4) * log(2) * exp(Pi*sqrt(7*n/3)/2) / (2^(3/2) * 7^(1/4) * Pi * n^(1/4)). - _Vaclav Kotesovec_, Oct 18 2018

%p b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(7*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, 7))))

%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]]] <= 7 &]]], {n, 43}] (* _Robert Price_, Jul 31 2020 *)

%Y Column k=7 of A210485.

%Y Cf. A261775.

%K nonn

%O 1,2

%A _Alois P. Heinz_, Oct 17 2018