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A320612 Number of parts in all partitions of n in which no part occurs more than nine times. 3
1, 3, 6, 12, 20, 35, 54, 86, 128, 182, 264, 376, 520, 718, 978, 1318, 1761, 2338, 3070, 4008, 5206, 6707, 8604, 10982, 13933, 17604, 22155, 27745, 34627, 43061, 53338, 65859, 81074, 99458, 121687, 148469, 180633, 219202, 265386, 320473, 386147, 464245, 556925 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..5000

FORMULA

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

MAPLE

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

      (l-> [0, l[1]*j]+l)(b(n-i*j, min(n-i*j, i-1))), j=0..min(n/i, 9))))

    end:

a:= n-> b(n$2)[2]:

seq(a(n), n=1..50);

MATHEMATICA

Table[Length[  Flatten[Select[IntegerPartitions[n], Max[Tally[#][[All, 2]]] <= 9 &]]], {n, 43}] (* Robert Price, Jul 31 2020 *)

CROSSREFS

Column k=9 of A210485.

Cf. A261776.

Sequence in context: A320609 A320610 A320611 * A320613 A006128 A247661

Adjacent sequences:  A320609 A320610 A320611 * A320613 A320614 A320615

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 17 2018

STATUS

approved

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Last modified July 28 11:50 EDT 2021. Contains 346328 sequences. (Running on oeis4.)