A364809 Number of partitions of n with at most five part sizes.

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 791, 1000, 1250, 1565, 1938, 2400, 2945, 3615, 4395, 5342, 6439, 7755, 9268, 11069, 13127, 15537, 18286, 21484, 25095, 29275, 33968, 39344, 45362, 52193, 59836, 68441, 78014, 88724, 100622, 113828

Offset

0,3

Links

Table of n, a(n) for n=0..50.

Formula

a(n) = Sum_{k=1..5} A116608(n,k).

Prog

(Python)
from sympy.utilities.iterables import partitions
def A364809(n): return sum(1 for p in partitions(n) if len(p)<=5) # Chai Wah Wu, Sep 14 2023

Crossrefs

Cf. A265250, A309058, A364793.

Cf. A116608, A365631.

Sequence in context: A046054 A242700 A242701 * A330642 A092885 A330643

Adjacent sequences: A364806 A364807 A364808 * A364810 A364811 A364812

Keyword

nonn

Author

Seiichi Manyama, Sep 14 2023

Status

approved