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A320609 Number of parts in all partitions of n in which no part occurs more than six times. 3
1, 3, 6, 12, 20, 35, 47, 78, 111, 165, 228, 330, 444, 614, 820, 1108, 1452, 1930, 2491, 3255, 4175, 5366, 6802, 8665, 10880, 13705, 17089, 21336, 26401, 32716, 40207, 49458, 60452, 73863, 89780, 109101, 131902, 159415, 191864, 230741, 276470, 331021, 394970 (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(7) * exp(2*Pi*sqrt(n/7)) / (2 * Pi * 7^(1/4) * n^(1/4)). - Vaclav Kotesovec, Oct 18 2018

MAPLE

b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(3*i*(i+1)<n, 0, add(

      (l-> [0, l[1]*j]+l)(b(n-i*j, min(n-i*j, i-1))), j=0..min(n/i, 6))))

    end:

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

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

MATHEMATICA

Table[Length[Flatten[Select[IntegerPartitions[n], Max[Tally[#][[All, 2]]] <= 6 &]]], {n, 43}] (* Robert Price, Jul 31 2020 *)

CROSSREFS

Column k=6 of A210485.

Cf. A035985.

Sequence in context: A096220 A034333 A182978 * A320610 A320611 A320612

Adjacent sequences:  A320606 A320607 A320608 * A320610 A320611 A320612

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 17 2018

STATUS

approved

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Last modified August 3 07:58 EDT 2021. Contains 346435 sequences. (Running on oeis4.)