A327477 Number of subsets of {1..n} containing n whose mean is not an element.

0, 0, 1, 2, 6, 12, 26, 54, 112, 226, 460, 930, 1876, 3780, 7606, 15288, 30720, 61680, 123786, 248346, 498072, 998636, 2001826, 4011942, 8039072, 16106124, 32263876, 64623330, 129424236, 259179060, 518975176, 1039104990, 2080374784, 4164816708, 8337289456

Offset: 0

Author

Gus Wiseman, Sep 13 2019

Keywords

• nonn

Examples

			The a(1) = 1 through a(5) = 12 subsets:
  {1,2}  {1,3}  {1,4}      {1,5}
         {2,3}  {2,4}      {2,5}
                {3,4}      {3,5}
                {1,2,4}    {4,5}
                {1,3,4}    {1,2,5}
                {1,2,3,4}  {1,4,5}
                           {2,3,5}
                           {2,4,5}
                           {1,2,3,5}
                           {1,2,4,5}
                           {1,3,4,5}
                           {2,3,4,5}
		

Crossrefs

Subsets whose mean is an element are A065795.

Subsets whose mean is not an element are A327471.

Subsets containing n whose mean is an element are A000016.

Cf. A007865, A051293, A082550, A135342, A240851, A324741, A327472.

Programs

Mathematica

Table[Length[Select[Subsets[Range[n]],MemberQ[#,n]&&!MemberQ[#,Mean[#]]&]],{n,0,10}]

Python

from sympy import totient, divisors
def A327477(n): return (1<>(~n&n-1).bit_length(),generator=True))//n if n else 0 # Chai Wah Wu, Feb 21 2023

Formula

From Alois P. Heinz, Feb 21 2023: (Start)

a(n) = A327471(n) - A327471(n-1) for n>=1.

a(n) = 2^(n-1) - A000016(n) for n>=1. (End)

Extensions

a(25)-a(34) from Alois P. Heinz, Feb 21 2023