A381358 Row sums of irregular triangle A381587.

1, 1, 2, 3, 5, 9, 15, 25, 41, 67, 109, 175, 277, 433, 671, 1035, 1595, 2463, 3817, 5937, 9259, 14457, 22569, 35193, 54795, 85195, 132333, 205471, 319069, 495699

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 sums [1, 1, 2, 3, 5, 9, 15, 25, ...].
		

Crossrefs

Cf. A381587, A381357.

Programs

PARI

\\ Print the row sums 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 sums of the first N rows
for(n=1, N, print1(vecsum(A[n]),", "))