cp's OEIS Frontend

A362046 Number of nonempty subsets of {1..n} with mean n/2.

%I A362046 #12 Apr 18 2023 17:33:01
%S A362046 0,0,1,1,3,3,9,8,25,23,75,68,235,213,759,695,2521,2325,8555,7941,
%T A362046 29503,27561,103129,96861,364547,344003,1300819,1232566,4679471,
%U A362046 4449849,16952161,16171117,61790441,59107889,226451035,217157068,833918839,801467551,3084255127
%N A362046 Number of nonempty subsets of {1..n} with mean n/2.
%F A362046 a(n) = (A070925(n) - 1)/2.
%F A362046 a(n) = A133406(n) - 1.
%F A362046 a(2n) = A212352(n) = A000980(n)/2 - 1.
%e A362046 The a(2) = 1 through a(7) = 8 subsets:
%e A362046   {1}  {1,2}  {2}      {1,4}      {3}          {1,6}
%e A362046               {1,3}    {2,3}      {1,5}        {2,5}
%e A362046               {1,2,3}  {1,2,3,4}  {2,4}        {3,4}
%e A362046                                   {1,2,6}      {1,2,4,7}
%e A362046                                   {1,3,5}      {1,2,5,6}
%e A362046                                   {2,3,4}      {1,3,4,6}
%e A362046                                   {1,2,3,6}    {2,3,4,5}
%e A362046                                   {1,2,4,5}    {1,2,3,4,5,6}
%e A362046                                   {1,2,3,4,5}
%t A362046 Table[Length[Select[Subsets[Range[n]],Mean[#]==n/2&]],{n,0,15}]
%Y A362046 Using range 0..n gives A070925.
%Y A362046 Including the empty set gives A133406.
%Y A362046 Even bisection is A212352.
%Y A362046 For median instead of mean we have A361801, the doubling of A079309.
%Y A362046 A version for partitions is A361853, for median A361849.
%Y A362046 A000980 counts nonempty subsets of {1..2n-1} with mean n.
%Y A362046 A007318 counts subsets by length.
%Y A362046 A067538 counts partitions with integer mean, strict A102627.
%Y A362046 A231147 appears to count subsets by median, full-steps A013580.
%Y A362046 A327475 counts subsets with integer mean, A000975 integer median.
%Y A362046 A327481 counts subsets by integer mean.
%Y A362046 Cf. A006134, A024718, A057552, A349156, A359893, A361654, A361864.
%K A362046 nonn
%O A362046 0,5
%A A362046 _Gus Wiseman_, Apr 12 2023