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

0,4

Links

Table of n, a(n) for n=0..34.

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)

Example

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}

Mathematica

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

Prog

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

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.

Sequence in context: A054454 A084170 A245264 * A350294 A052971 A364423

Adjacent sequences: A327474 A327475 A327476 * A327478 A327479 A327480

Keyword

nonn

Author

Gus Wiseman, Sep 13 2019

Extensions

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

Status

approved