A096137 Table read by rows: row n contains the sum of each nonempty subset of {1, 2, ..., n}. In each row, the sums are arranged in ascending order.

1, 1, 2, 3, 1, 2, 3, 3, 4, 5, 6, 1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 9, 10, 1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 12, 12, 13, 14, 15, 1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12

Offset

1,3

Comments

The n-th row has 2^n-1 members. A001788 gives the row sums. The sums of the k-element subsets of {1, 2, ..., n} add up to A094305(n-1, k-1).

Links

Alois P. Heinz, Rows n = 1..15, flattened

Example

The nonempty subsets of {1, 2, 3} are {1}, {2}, {3}, {1,2}, {1,3}, {2,3} and {1,2,3}, which have sums 1, 2, 3, 3, 4, 5 and 6 respectively, so these are the terms of row 3.
Triangle T(n,k) begins:
  1;
  1, 2, 3;
  1, 2, 3, 3, 4, 5, 6;
  1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 9, 10;
  ...

Maple

T:= proc(n) option remember; `if`(n=0, [][], subsop(1=[][],
      sort(map(x-> (x, x+n), [0, T(n-1)])))[])
    end:
seq(T(n), n=1..7);  # Alois P. Heinz, Jul 24 2019

Mathematica

T[n_] := T[n] = Total /@ Subsets[Range[n], {1, n}] // Sort;
Array[T, 7] // Flatten (* Jean-François Alcover, Feb 14 2021 *)

Crossrefs

Cf. A001788, A094305.

Sequence in context: A255890 A194300 A065365 * A282905 A063274 A274459

Adjacent sequences: A096134 A096135 A096136 * A096138 A096139 A096140

Keyword

nonn,easy,look,tabf

Author

Amarnath Murthy, Jul 06 2004

Extensions

Edited and extended by David Wasserman, Oct 04 2007

Status

approved