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
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.
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}]