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Number of partitions of n with at most five part sizes.
3

%I #23 Sep 14 2023 12:37:52

%S 1,1,2,3,5,7,11,15,22,30,42,56,77,101,135,176,231,297,385,490,627,791,

%T 1000,1250,1565,1938,2400,2945,3615,4395,5342,6439,7755,9268,11069,

%U 13127,15537,18286,21484,25095,29275,33968,39344,45362,52193,59836,68441,78014,88724,100622,113828

%N Number of partitions of n with at most five part sizes.

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

%o (Python)

%o from sympy.utilities.iterables import partitions

%o def A364809(n): return sum(1 for p in partitions(n) if len(p)<=5) # _Chai Wah Wu_, Sep 14 2023

%Y Cf. A265250, A309058, A364793.

%Y Cf. A116608, A365631.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Sep 14 2023