A181047 Number of length-n sequences A over {1,2,3} with the property that all of r(A), r(r(A)), etc. are over {1,2,3}, where r is the sequence obtained by taking the run lengths in A.

1, 3, 9, 27, 54, 180, 426, 1080, 2724, 6300, 16512, 42432, 98064, 248256, 616656, 1509888, 3767040, 9389376, 23549376, 58493760, 140807232, 336314880, 806979456

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Example

For example, the run-lengths in 1333 are 13, then the run-lengths of this is 11, then the run-lengths of this is 2, then the run-lengths of this is 1, so this sequence is counted in a(4).

Prog

(Python)
from itertools import groupby, product
def r(w):
    return [len(list(g)) for k, g in groupby(w)]
def c(w):
    while (rw:=r(w)) != w:
        if not set(rw) <= {1, 2, 3}: return False
        w = rw
    return True
def a(n):
    if n == 0: return 1
    return 3*sum(1 for w in product((1, 2, 3), repeat=n-1) if c((1, )+w))
print([a(n) for n in range(14)]) # Michael S. Branicky, Jan 06 2026

Crossrefs

Sequence in context: A163791 A248078 A057829 * A014948 A093665 A093546

Adjacent sequences: A181044 A181045 A181046 * A181048 A181049 A181050

Keyword

nonn,hard,more

Author

Jeffrey Shallit, Oct 01 2010

Extensions

a(0)-a(10) confirmed and a(11)-a(14) added by John W. Layman, Oct 07 2010

a(15)-a(16) from Alois P. Heinz, Oct 16 2011

a(17)-a(22) from Michael S. Branicky, Jan 06 2026

Status

approved