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

Author

Clark Kimberling, Dec 20 2024

Keywords

• nonn
• tabf

Comments

See A378282 for a guide to related arrays and sequences.

Examples

			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).
		

Crossrefs

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

Programs

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 *)