A327471 Number of subsets of {1..n} not containing their mean.

1, 1, 2, 4, 10, 22, 48, 102, 214, 440, 900, 1830, 3706, 7486, 15092, 30380, 61100, 122780, 246566, 494912, 992984, 1991620, 3993446, 8005388, 16044460, 32150584, 64414460, 129037790, 258462026, 517641086, 1036616262, 2075721252, 4156096036, 8320912744, 16658202200

Offset: 0

Author

Gus Wiseman, Sep 12 2019

Keywords

• nonn

Examples

			The a(1) = 1 through a(5) = 22 subsets:
  {}  {}     {}     {}         {}
      {1,2}  {1,2}  {1,2}      {1,2}
             {1,3}  {1,3}      {1,3}
             {2,3}  {1,4}      {1,4}
                    {2,3}      {1,5}
                    {2,4}      {2,3}
                    {3,4}      {2,4}
                    {1,2,4}    {2,5}
                    {1,3,4}    {3,4}
                    {1,2,3,4}  {3,5}
                               {4,5}
                               {1,2,4}
                               {1,2,5}
                               {1,3,4}
                               {1,4,5}
                               {2,3,5}
                               {2,4,5}
                               {1,2,3,4}
                               {1,2,3,5}
                               {1,2,4,5}
                               {1,3,4,5}
                               {2,3,4,5}
		

Crossrefs

Subsets containing their mean are A065795.

Subsets containing n but not their mean are A327477.

Partitions not containing their mean are A327472.

Strict partitions not containing their mean are A240851.

Cf. A000016, A007865, A051293, A067538, A082550, A114639, A135342, A324741, A327476.

Programs

Mathematica

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

Python

from sympy import totient, divisors
def A327471(n): return (1<>(~k&k-1).bit_length(),generator=True))<<1)//k for k in range(1,n+1))>>1) # Chai Wah Wu, Feb 22 2023

Formula

a(n) = 2^n - A065795(n). - Alois P. Heinz, Sep 13 2019

Extensions

More terms from Alois P. Heinz, Sep 13 2019