A106599 Irregular triangle read by rows generated by the morphism 1->56, 2->4, 3->5, 4->2, 5->3, 6->12 starting from 1.

1, 5, 6, 3, 1, 2, 5, 5, 6, 4, 3, 3, 1, 2, 2, 5, 5, 5, 6, 4, 4, 3, 3, 3, 1, 2, 2, 2, 5, 5, 5, 5, 6, 4, 4, 4, 3, 3, 3, 3, 1, 2, 2, 2, 2, 5, 5, 5, 5, 5, 6, 4, 4, 4, 4, 3, 3, 3, 3, 3, 1, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 6, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 1, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 6, 4, 4, 4, 4, 4, 4

Offset

0,2

Links

Alois P. Heinz, Rows n = 0..150, flattened

Curtis T. McMullen, Prym varieties and Teichmüller curves, Duke Math. J. 133(3) (2006), 569-590.

Example

Triangle begins:
  1;
  5, 6;
  3, 1, 2;
  5, 5, 6, 4;
  3, 3, 1, 2, 2;
  5, 5, 5, 6, 4, 4;
  3, 3, 3, 1, 2, 2, 2;
  5, 5, 5, 5, 6, 4, 4, 4;
  ...

Maple

f:= n-> [[5, 6], [4], [5], [2], [3], [1, 2]][n][]:
T:= proc(n) option remember; `if`(n=0, 1, map(f, [T(n-1)])[]) end:
seq(T(n), n=0..13);  # Alois P. Heinz, May 11 2026

Mathematica

SubstitutionSystem[{1 -> {5, 6}, 2 -> {4}, 3 -> {5}, 4 -> {2}, 5 -> {3}, 6 -> {1, 2}}, {1}, 13] (* Paolo Xausa, May 12 2026 *)

Crossrefs

Cf. A106591, A106592.

Sequence in context: A226533 A011499 A242813 * A342015 A222466 A195448

Adjacent sequences: A106596 A106597 A106598 * A106600 A106601 A106602

Keyword

nonn,tabl,easy

Author

Roger L. Bagula, May 10 2005

Extensions

Edited by Sean A. Irvine, May 11 2026

Status

approved