A212352 - OEIS

%I #11 Apr 18 2023 09:42:40

%S 0,1,3,9,25,75,235,759,2521,8555,29503,103129,364547,1300819,4679471,

%T 16952161,61790441,226451035,833918839,3084255127,11451630043,

%U 42669225171,159497648599,597950875255,2247724108771,8470205600639

%N Row sums of A047997.

%C Also the number of nonempty subsets of {1..2n} with mean n, even bisection of A362046. - _Gus Wiseman_, Apr 15 2023

%F From _Gus Wiseman_, Apr 15 2023: (Start)

%F a(n) = A000980(n)/2 - 1.

%F a(n) = A047653(n) - 1.

%F a(n) = A133406(2n+1) - 1.

%F a(n) = A362046(2n).

%F (End)

%e From _Gus Wiseman_, Apr 15 2023: (Start)

%e The a(1) = 1 through a(3) = 9 subsets:

%e   {1}  {2}      {3}

%e        {1,3}    {1,5}

%e        {1,2,3}  {2,4}

%e                 {1,2,6}

%e                 {1,3,5}

%e                 {2,3,4}

%e                 {1,2,3,6}

%e                 {1,2,4,5}

%e                 {1,2,3,4,5}

%e (End)

%t Table[Length[Select[Subsets[Range[2n]],Mean[#]==n&]],{n,0,6}] (* _Gus Wiseman_, Apr 15 2023 *)

%Y Equals A047653(n) - 1.

%Y Row sums of A047997.

%Y For median instead of mean we have A079309, bisection of A361801.

%Y Even bisection of A362046, zero-based version A070925.

%Y A000980 counts nonempty subsets of {1..2n-1} with mean n.

%Y A007318 counts subsets by length.

%Y A327475 counts subsets with integer mean.

%Y A327481 counts subsets by mean.

%Y Cf. A000975, A013580, A024718, A057552, A133406, A361866.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, May 16 2012