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A327484 Number of integer partitions of 2^n whose mean is a power of 2. 4
1, 2, 4, 11, 66, 1417, 178803, 275379307, 15254411521973, 108800468645440803267, 964567296140908420613296779144, 219614169629364529542990295052656098001967511, 38626966436500261962963100479469496821891576834974275502742922521 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Number of partitions of 2^n whose number of parts is a power of 2. - Chai Wah Wu, Sep 21 2023
LINKS
Chai Wah Wu, Table of n, a(n) for n = 0..15 (n = 0..13 from Alois P. Heinz)
EXAMPLE
The a(0) = 1 through a(3) = 11 partitions:
(1) (2) (4) (8)
(11) (22) (44)
(31) (53)
(1111) (62)
(71)
(2222)
(3221)
(3311)
(4211)
(5111)
(11111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[2^n], IntegerQ[Mean[#]]&]], {n, 0, 5}]
PROG
(Python)
from sympy.utilities.iterables import partitions
def A327484(n): return sum(1 for s, p in partitions(1<<n, size=True) if not(s&-s)^s) # Chai Wah Wu, Sep 21 2023
(Python)
# uses A008284_T
def A327484(n): return sum(A008284_T(1<<n, 1<<k) for k in range(n+1)) # Chai Wah Wu, Sep 21 2023
CROSSREFS
Row sums of A327483.
Sequence in context: A156434 A007903 A182100 * A006894 A193565 A198864
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 13 2019
EXTENSIONS
a(7) from Chai Wah Wu, Sep 14 2019
a(8)-a(11) from Alois P. Heinz, Sep 21 2023
a(12) from Chai Wah Wu, Sep 21 2023
STATUS
approved

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Last modified April 18 09:47 EDT 2024. Contains 371779 sequences. (Running on oeis4.)