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

1,3

Comments

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

Links

Table of n, a(n) for n=1..30.

Example

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, ...].

Prog

(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]), ", "))

Crossrefs

Cf. A381587, A381357.

Sequence in context: A323475 A097083 A268709 * A326024 A200047 A147877

Adjacent sequences: A381354 A381356 A381357 * A381360 A381362 A381363

Keyword

nonn,more,new

Author

Paul D. Hanna, Mar 03 2025

Status

approved