A365631 Number of partitions of n with exactly five part sizes.
1, 2, 5, 10, 20, 36, 58, 95, 147, 222, 323, 462, 636, 889, 1184, 1584, 2060, 2686, 3403, 4353, 5433, 6768, 8319, 10230, 12363, 15011, 17943, 21467, 25403, 30044, 35231, 41294, 48002, 55718, 64328, 74086, 84880, 97071, 110607, 125692, 142313, 160728, 181112, 203438, 228124
Offset: 15
Keywords
Examples
a(16) = 2 because we have 6+4+3+2+1, 5+4+3+2+1+1.
Links
- Alois P. Heinz, Table of n, a(n) for n = 15..5000
Crossrefs
Programs
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Maple
# Using function P from A365676: A365631 := n -> P(n, 5, n): seq(A365631(n), n = 15..59); # Peter Luschny, Sep 15 2023
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Python
from sympy.utilities.iterables import partitions def A365631(n): return sum(1 for p in partitions(n) if len(p)==5) # Chai Wah Wu, Sep 14 2023
Formula
G.f.: Sum_{0
A364793 Number of partitions of n with at most four part sizes.
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 175, 229, 292, 375, 470, 591, 733, 905, 1103, 1343, 1615, 1938, 2309, 2726, 3211, 3758, 4379, 5069, 5865, 6716, 7694, 8769, 9967, 11254, 12732, 14264, 16025, 17877, 19959, 22149, 24605, 27147, 30012, 33006, 36294, 39742, 43573, 47524
Offset: 0
Keywords
Programs
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Python
from sympy.utilities.iterables import partitions def A364793(n): return sum(1 for p in partitions(n) if len(p)<=4) # Chai Wah Wu, Sep 14 2023
Formula
a(n) = Sum_{k=1..4} A116608(n,k).