A369526 Table read by upward antidiagonals: T(n,k) = number of nonempty subsets of {1..n} for which the average is the k-th power of an integer.

1, 2, 1, 5, 1, 1, 8, 1, 1, 1, 15, 2, 1, 1, 1, 26, 4, 1, 1, 1, 1, 45, 10, 1, 1, 1, 1, 1, 76, 20, 1, 1, 1, 1, 1, 1, 135, 26, 1, 1, 1, 1, 1, 1, 1, 238, 31, 2, 1, 1, 1, 1, 1, 1, 1, 425, 35, 4, 1, 1, 1, 1, 1, 1, 1, 1, 768, 41, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

1,2

Links

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

Example

T(8,3) = 2 subsets {1}, {8} of {1..8} with a cube average.
Table begins:
       1,     1,    1,   1, 1, ...
       2,     1,    1,   1, 1, ...
       5,     1,    1,   1, 1, ...
       8,     2,    1,   1, 1, ...
      15,     4,    1,   1, 1, ...
      26,    10,    1,   1, 1, ...
      45,    20,    1,   1, 1, ...
      76,    26,    2,   1, 1, ...
     135,    31,    4,   1, 1, ...
     238,    35,   10,   1, 1, ...
     425,    41,   32,   1, 1, ...
     768,    63,  106,   1, 1, ...
    1399,   143,  310,   1, 1, ...
    2570,   399,  760,   1, 1, ...
    4761,  1083, 1520,   1, 1, ...
    8856,  2554, 2522,   2, 1, ...
   16567,  5078, 3630,   4, 1, ...
   31138,  8596, 4708,  10, 1, ...
   58733, 12772, 5670,  32, 1, ...
  111164, 17222, 6484, 118, 1, ...

Crossrefs

Cf. A051293, A369391.

Sequence in context: A256541 A342919 A066421 * A206563 A299779 A323954

Adjacent sequences: A369523 A369524 A369525 * A369527 A369528 A369529

Keyword

tabl,nonn

Author

Jean-Marc Rebert, Jan 25 2024

Status

approved