A381357 Row lengths of irregular triangle A381587.

1, 1, 1, 2, 4, 6, 10, 16, 26, 42, 66, 102, 156, 238, 364, 560, 868, 1354, 2120, 3322, 5198, 8112, 12624, 19602, 30400, 47138, 73138, 113598, 176630, 274858

Offset: 1

Author

Paul D. Hanna, Mar 03 2025

Keywords

• nonn
• more

Comments

If it exists, what is the limit of a(n)^(1/n) as n increases?

Examples

			Row n+1 of irregular triangle A381587 equals the run lengths of the first n rows of the triangle (flattened) when read in reverse order, starting with
  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; ...
This sequence gives the row lengths [1, 1, 1, 2, 4, 6, 10, 16, ...].
		

Crossrefs

Cf. A381587, A381358.

Programs

PARI

\\ Print the row lengths of irregular triangle A381587
\\ 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=25; 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]); );}
\\ Print the row lengths of the first N rows
for(n=1, N, print1(#A[n],", "))