OFFSET
1,2
COMMENTS
This sequence appears to equal the RUNS transform of A306346.
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..5000
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
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.
PROG
(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], ", "))
CROSSREFS
KEYWORD
nonn,new
AUTHOR
Paul D. Hanna, Mar 03 2025
STATUS
approved