A384002 Let S(n,j,k), j = 1..n, k = 1..A024718(n), where row 1 = {(0),(1)}, and row n = union of n-tuples whose sum m < n, and the n-tuples formed by appending m to the (n-1)-tuples in row n-1. Then T(n,j) = j-th tuple in row n of S read as a base n+1 number expressed in decimal.

0, 1, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 6, 8, 9, 16, 17, 18, 20, 21, 32, 0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 15, 16, 25, 26, 27, 28, 30, 31, 32, 35, 36, 50, 51, 52, 55, 56, 75, 125, 126, 127, 128, 130, 131, 132, 135, 136, 150, 151, 152, 155, 156, 175, 250, 251, 252, 255, 275, 375

Offset: 1

Author

Michael De Vlieger, May 21 2025

Keywords

• nonn
• tabf
• base
• easy
• look

Examples

			Table begins:
  1:  0, 1;
  2:  0, 1, 2, 3, 4;
  3:  0, 1, 2, 3, 4, 5, 6, 8, 9, 16, 17, 18, 20, 21, 32;
  4:  0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 15, 16, 25, 26, 27, 28, 30, 31, 32,
      35, 36, 50, 51, 52, 55, 56, 75, 125, 126, 127, 128, 130, 131, 132, 135,
      136, 150, 151, 152, 155, 156, 175, 250, 251, 252, 255, 275, 375;
  etc.
Row 2 of S is {(0, 0), (0, 1), (0, 2), (1, 0), (1, 1)}. Reading the tuples in row 2 as a base 3 number, we have row 2 of this sequence.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..12029 (rows n = 1..8, flattened).
• Michael De Vlieger, Log log scatterplot of a(n) for n = 1..2479069 (rows n = 1..12), ignoring a(n) = 0.

Crossrefs

Cf. A024718, A384001.

Programs

Mathematica

nn = 8; w[0] = {{0}};
Do[If[n == 1, Set[w[1], {{0}, {1}}],
  Set[w[n], Union@ Join[Select[Tuples[Range[0, n - 1], n], Total[#] < n &],
    Map[Append[#, n - Total[#]] &, w[n - 1] ] ] ] ], {n, nn}];
Table[Map[FromDigits[#, n + 1] &, w[n]], {n, 0, nn}]

Formula

T(n,j) = base n+1 expansion of j-th tuple in row n of A384001.

Length of row n = A024718(n).