A378303 Irregular triangular T: (row 1) = (1); (row n+1) = inverse runlength sequence of row n, starting with 1 if r = 3k for some k, and 2 otherwise. See Comments.

1, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2

Offset

1,2

Comments

See A378282 for a guide to related arrays and sequences.

Links

Table of n, a(n) for n=1..86.

Example

First nine rows:
   1
   2
   2, 2
   1, 1, 2, 2
   2, 1, 2, 2, 1, 1
   2, 2, 1, 2, 2, 1, 1, 2, 1
   1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1
   2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1
   2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2
(row 9) = (2,2,1,2,2,1,...) has runlength sequence (2,1,2,2,...) = (row 8).

Mathematica

invRE[seq_, k_] := Flatten[Map[ConstantArray[#[[2]], #[[1]]] &,
    Partition[Riffle[seq, {k, 2 - Mod[k + 1, 2]}, {2, -1, 2}], 2]]];
row1 = {1}; rows = {row1};
col = PadRight[{}, 18, {1, 2, 2}]
Do[AppendTo[rows, invRE[Last[rows], col[[n]]]], {n, 2, Length[col]}]
rows // ColumnForm  (* array *)
Flatten[rows]  (* sequence *)
(* Peter J. C. Moses, Nov 21 2024 *)

Crossrefs

Cf. A378282, A378304, A378305, A378306, A378307 (row lengths)

Sequence in context: A037811 A091237 A143477 * A214774 A320107 A190321

Adjacent sequences: A378300 A378301 A378302 * A378304 A378305 A378306

Keyword

nonn,tabf

Author

Clark Kimberling, Dec 20 2024

Status

approved