A327481 Triangle read by rows where T(n,k) is the number of nonempty subsets of {1..n} with mean k.

1, 1, 1, 1, 3, 1, 1, 3, 3, 1, 1, 3, 7, 3, 1, 1, 3, 9, 9, 3, 1, 1, 3, 9, 19, 9, 3, 1, 1, 3, 9, 25, 25, 9, 3, 1, 1, 3, 9, 29, 51, 29, 9, 3, 1, 1, 3, 9, 31, 75, 75, 31, 9, 3, 1, 1, 3, 9, 31, 93, 151, 93, 31, 9, 3, 1, 1, 3, 9, 31, 105, 235, 235, 105, 31, 9, 3, 1

Offset

1,5

Comments

All terms are odd.

Links

Table of n, a(n) for n=1..78.

Example

Triangle begins:
                         1
                       1   1
                     1   3   1
                   1   3   3   1
                 1   3   7   3   1
               1   3   9   9   3   1
             1   3   9  19   9   3   1
           1   3   9  25  25   9   3   1
         1   3   9  29  51  29   9   3   1
       1   3   9  31  75  75  31   9   3   1
     1   3   9  31  93 151  93  31   9   3   1
   1   3   9  31 105 235 235 105  31   9   3   1
The subsets counted in row n = 5:
  {1}  {2}      {3}          {4}      {5}
       {1,3}    {1,5}        {3,5}
       {1,2,3}  {2,4}        {3,4,5}
                {1,3,5}
                {2,3,4}
                {1,2,4,5}
                {1,2,3,4,5}

Mathematica

Table[Length[Select[Subsets[Range[n]], Mean[#]==k&]], {n, 10}, {k, n}]

Crossrefs

Row sums are A051293.

The sequence of rows converges to A066571.

The version for partitions is A327482.

Cf. A000016, A063776, A065795, A135342, A327474, A327475, A327483, A327484.

Sequence in context: A157454 A106255 A143086 * A152714 A174546 A134444

Adjacent sequences: A327478 A327479 A327480 * A327482 A327483 A327484

Keyword

nonn,tabl

Author

Gus Wiseman, Sep 13 2019

Status

approved