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

Author

Seiichi Manyama, Sep 14 2023

Keywords

• nonn

Crossrefs

Cf. A265250, A309058, A364793.

Cf. A116608, A365631.

Programs

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

Formula

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