A381356 Limit of rows in irregular triangle A381587.

1, 3, 1, 3, 1, 3, 1, 1, 1, 5, 1, 1, 1, 1, 1, 7, 1, 3, 1, 1, 1, 1, 1, 7, 1, 1, 1, 5, 1, 3, 1, 1, 1, 1, 1, 7, 1, 1, 1, 3, 1, 5, 1, 1, 1, 5, 1, 3, 1, 1, 1, 1, 1, 7, 1, 1, 1, 3, 1, 1, 1, 3, 1, 5, 1, 1, 1, 3, 1, 5, 1, 1, 1, 5, 1, 3, 1, 1, 1, 1, 1, 7, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 5

Offset: 1

Author

Paul D. Hanna, Mar 03 2025

Keywords

• nonn

Comments

This sequence appears to equal the RUNS transform of A306346.

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
n = 1: [1];
n = 2: [1];
n = 3: [2];
n = 4: [1, 2];
n = 5: [1, 1, 1, 2];
n = 6: [1, 3, 1, 1, 1, 2];
n = 7: [1, 3, 1, 1, 1, 3, 1, 1, 1, 2];
n = 8: [1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 2];
n = 9: [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];
n = 10: [1, 3, 1, 3, 1, 3, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 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];
n = 11: [1, 3, 1, 3, 1, 3, 1, 1, 1, 5, 1, 1, 1, 1, 1, 7, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 3, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 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];
n = 12: [1, 3, 1, 3, 1, 3, 1, 1, 1, 5, 1, 1, 1, 1, 1, 7, 1, 3, 1, 1, 1, 1, 1, 7, 1, 1, 1, 5, 1, 3, 1, 1, 1, 1, 1, 1, ...];
...
This sequence gives the limit of the rows.
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A381587, A306346.

Programs

PARI

\\ Print the limit of the rows in 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 initial terms of the limit of the rows
\\ (row 25 has 10797 terms of the limit of rows sequence)
for(n=1,120, print1(A[25][n],", "))