A327484 Number of integer partitions of 2^n whose mean is a power of 2.

1, 2, 4, 11, 66, 1417, 178803, 275379307, 15254411521973, 108800468645440803267, 964567296140908420613296779144, 219614169629364529542990295052656098001967511, 38626966436500261962963100479469496821891576834974275502742922521

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.

Cf. A067538, A068413, A135342, A237984, A327474, A327481, A327482.

Sequence in context: A156434 A007903 A182100 * A006894 A193565 A198864

Adjacent sequences: A327481 A327482 A327483 * A327485 A327486 A327487

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