OFFSET
1,4
COMMENTS
This is the number of distinct binary words w of length n that eventually cycle under the Post tag system (see A284116, A289670) reduced to take into account the observation made by Don Reble that (if the bits of w are labeled from the left starting at bit 0) bits 1,2,4,5,7,8,... (not a multiple of 3) are "junk DNA" and have no effect on the outcome.
PROG
(Python)
from __future__ import division
def A289677(n):
c, k, r, n2, cs, ts = 0, 1+(n-1)//3, 2**((n-1) % 3), 2**(n-1), set(), set()
for i in range(2**k):
j, l = int(bin(i)[2:], 8)*r, n2
traj = set([(l, j)])
while True:
if j >= l:
j = j*16+13
l *= 2
else:
j *= 4
l //= 2
if l == 0:
ts |= traj
break
j %= 2*l
if (l, j) in traj:
c += 1
cs |= traj
break
if (l, j) in cs:
c += 1
break
if (l, j) in ts:
break
traj.add((l, j))
return c # Chai Wah Wu, Aug 03 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 01 2017
STATUS
approved