A030717 The first list after the following procedure: starting with a list [1] and an empty list, repeatedly add the distinct values already in the first list in ascending order to the second list and add the corresponding frequencies of those values to the first list.

1, 1, 2, 2, 1, 3, 2, 3, 3, 1, 4, 3, 3, 4, 3, 5, 1, 5, 3, 6, 2, 1, 6, 4, 7, 2, 2, 1, 7, 6, 7, 3, 2, 2, 1, 8, 8, 8, 3, 2, 3, 3, 8, 9, 11, 3, 2, 3, 3, 3, 8, 10, 15, 3, 2, 3, 3, 4, 1, 1, 10, 11, 18, 4, 2, 3, 3, 5, 1, 1, 1, 1, 14, 12, 20, 5, 3, 3, 3, 5, 1, 2, 2, 1

Offset

1,3

Comments

The clarifying comment that follows refers to the old name, which was: Row 1, where, at stage k>1, write i in row 1 and j in row 2, where i is the number of j's in row 1, for j=1,2,...,m, where m=max number in row 1 from stages 1 to k-1; state 1 is 1 in row 1.

Numbers j for which the count is 0 are omitted, cf. A333867 for the corresponding sequence where they are included. - Sean A. Irvine, Apr 08 2020

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Sean A. Irvine)

Sean A. Irvine, Java program (github)

Example

First list begins:
  1;
  1;
  2;
  2, 1;
  3, 2;
  3, 3,  1;
  4, 3,  3;
  4, 3,  5, 1;
  5, 3,  6, 2, 1;
  6, 4,  7, 2, 2, 1;
  7, 6,  7, 3, 2, 2, 1;
  8, 8,  8, 3, 2, 3, 3;
  8, 9, 11, 3, 2, 3, 3, 3;

Mathematica

t = {{1}}; Do[AppendTo[t, BinCounts[#, {1, Max[#] + 1}] &[Flatten[t]]], {25}];
DeleteCases[Flatten[t], 0]  (* Peter J. C. Moses, Apr 09 2020 *)

Crossrefs

Cf. A030718 (2nd list), A030719 (row lengths), A006920.

Cf. A030707 (repeatedly adds values and frequencies from both lists).

Cf. A333867 (0 counts included, but not the counts of 0s).

Cf. A030723, A030724, A030725, A030726, A358423, A358424, A358425.

Sequence in context: A349526 A329949 A333867 * A280716 A319444 A071285

Adjacent sequences: A030714 A030715 A030716 * A030718 A030719 A030720

Keyword

nonn,tabf,nice

Author

Clark Kimberling

Extensions

More terms from Franklin T. Adams-Watters, Dec 14 2006

Rolled back to original definition and data by Sean A. Irvine, Apr 08 2020

Name revised in line with A030777 by Peter Munn, Oct 11 2022

Status

approved