cp's OEIS Frontend

A212352 Row sums of A047997.

%I A212352 #11 Apr 18 2023 09:42:40
%S A212352 0,1,3,9,25,75,235,759,2521,8555,29503,103129,364547,1300819,4679471,
%T A212352 16952161,61790441,226451035,833918839,3084255127,11451630043,
%U A212352 42669225171,159497648599,597950875255,2247724108771,8470205600639
%N A212352 Row sums of A047997.
%C A212352 Also the number of nonempty subsets of {1..2n} with mean n, even bisection of A362046. - _Gus Wiseman_, Apr 15 2023
%F A212352 From _Gus Wiseman_, Apr 15 2023: (Start)
%F A212352 a(n) = A000980(n)/2 - 1.
%F A212352 a(n) = A047653(n) - 1.
%F A212352 a(n) = A133406(2n+1) - 1.
%F A212352 a(n) = A362046(2n).
%F A212352 (End)
%e A212352 From _Gus Wiseman_, Apr 15 2023: (Start)
%e A212352 The a(1) = 1 through a(3) = 9 subsets:
%e A212352   {1}  {2}      {3}
%e A212352        {1,3}    {1,5}
%e A212352        {1,2,3}  {2,4}
%e A212352                 {1,2,6}
%e A212352                 {1,3,5}
%e A212352                 {2,3,4}
%e A212352                 {1,2,3,6}
%e A212352                 {1,2,4,5}
%e A212352                 {1,2,3,4,5}
%e A212352 (End)
%t A212352 Table[Length[Select[Subsets[Range[2n]],Mean[#]==n&]],{n,0,6}] (* _Gus Wiseman_, Apr 15 2023 *)
%Y A212352 Equals A047653(n) - 1.
%Y A212352 Row sums of A047997.
%Y A212352 For median instead of mean we have A079309, bisection of A361801.
%Y A212352 Even bisection of A362046, zero-based version A070925.
%Y A212352 A000980 counts nonempty subsets of {1..2n-1} with mean n.
%Y A212352 A007318 counts subsets by length.
%Y A212352 A327475 counts subsets with integer mean.
%Y A212352 A327481 counts subsets by mean.
%Y A212352 Cf. A000975, A013580, A024718, A057552, A133406, A361866.
%K A212352 nonn
%O A212352 0,3
%A A212352 _N. J. A. Sloane_, May 16 2012