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

1,5

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.

Formula

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

Length of row n = A024718(n).

Example

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.

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}]

Crossrefs

Cf. A024718, A384001.

Sequence in context: A060511 A082853 A230431 * A394562 A394758 A190886

Adjacent sequences: A383999 A384000 A384001 * A384003 A384004 A384005

Keyword

nonn,tabf,base,easy,look

Author

Michael De Vlieger, May 21 2025

Status

approved