A327484 - OEIS

%I #26 Sep 22 2023 02:12:06

%S 1,2,4,11,66,1417,178803,275379307,15254411521973,

%T 108800468645440803267,964567296140908420613296779144,

%U 219614169629364529542990295052656098001967511,38626966436500261962963100479469496821891576834974275502742922521

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

%C Number of partitions of 2^n whose number of parts is a power of 2. - _Chai Wah Wu_, Sep 21 2023

%H Chai Wah Wu, <a href="/A327484/b327484.txt">Table of n, a(n) for n = 0..15</a> (n = 0..13 from Alois P. Heinz)

%e The a(0) = 1 through a(3) = 11 partitions:

%e   (1)  (2)   (4)     (8)

%e        (11)  (22)    (44)

%e              (31)    (53)

%e              (1111)  (62)

%e                      (71)

%e                      (2222)

%e                      (3221)

%e                      (3311)

%e                      (4211)

%e                      (5111)

%e                      (11111111)

%t Table[Length[Select[IntegerPartitions[2^n],IntegerQ[Mean[#]]&]],{n,0,5}]

%o (Python)

%o from sympy.utilities.iterables import partitions

%o 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

%o (Python)

%o # uses A008284_T

%o def A327484(n): return sum(A008284_T(1<<n,1<<k) for k in range(n+1)) # _Chai Wah Wu_, Sep 21 2023

%Y Row sums of A327483.

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

%K nonn

%O 0,2

%A _Gus Wiseman_, Sep 13 2019

%E a(7) from _Chai Wah Wu_, Sep 14 2019

%E a(8)-a(11) from _Alois P. Heinz_, Sep 21 2023

%E a(12) from _Chai Wah Wu_, Sep 21 2023