A381587 a(1) = 1; thereafter the sequence is extended by iteratively appending the run length transform of the reverse of the sequence thus far.

1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 1, 2, 1, 3, 1, 1, 1, 3, 1, 1, 1, 2, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 2, 1, 3, 1, 3, 1, 3, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 2, 1, 3, 1, 3, 1, 3, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3

Offset: 1

Author

Neal Gersh Tolunsky, Feb 27 2025

Keywords

• tabf
• nonn

Comments

The run length transform replaces each run of consecutive equal values with a single value representing the length of that run.

Is 2 the greatest even number in the sequence?

It appears that the limit of the rows read in reverse equals A306346 (ignoring the initial terms). - Paul D. Hanna, Mar 03 2025

Examples

			Irregular triangle begins:
  1;
  1;
  2;
  1,2;
  1,1,1,2;
  1,3,1,1,1,2;
  1,3,1,1,1,3,1,1,1,2;
  1,3,1,3,1,1,1,3,1,1,1,3,1,1,1,2;
  1,3,1,3,1,3,1,1,1,1,1,3,1,3,1,1,1,3,1,1,1,3,1,1,1,2;
  ...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..9259 (first 20 rows)

Crossrefs

Cf. A381357 (row lengths), A381358 (row sums), A381356 (limit of rows), A306346.

Cf. A306211.

Programs

PARI

\\ From Paul D. Hanna, Mar 03 2025: (Start)
\\ RUNS(V) Returns vector of run lengths in vector V:
{RUNS(V) = my(R=[],c=1);if(#V>1, for(n=2,#V, if(V[n]==V[n-1], c=c+1, R=concat(R,c); c=1))); R=concat(R,c)}
\\ REV(V) Reverses order of vector V:
{REV(V) = Vec(Polrev(Ser(V)))}
\\ Generates N rows as a vector A of row vectors
{N=15; A=vector(N);A[1]=[1];A[2]=[1];A[3]=[2];
for(n=3,#A-1, A[n+1] = concat(RUNS(REV(A[n])),A[n]);); A}
for(n=1,N,print(A[n])) \\ Print N rows of this triangle (End)