A289676 a(n) = A289670(n)/2^f(n), where f(n) = 2*floor((n-1)/3) + ((n+2) mod 3).

2, 1, 1, 2, 2, 1, 4, 4, 3, 5, 4, 3, 10, 13, 12, 21, 18, 20, 43, 40, 39, 85, 71, 64, 146, 132, 116, 250, 231, 210, 462, 459, 438, 960, 990, 966, 2069, 2114, 2089, 4296, 4237, 4155, 8485, 8234, 8032, 16496, 16054, 15657, 32041, 31280, 30325, 61700, 60252, 58379, 118357, 115810, 112885

Offset

1,1

Comments

This is the number of distinct binary words w of length n that terminate 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.

Links

Table of n, a(n) for n=1..57.

Prog

(Python)
from __future__ import division
def A289676(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:
                c += 1
                ts |= traj
                break
            j %= 2*l
            if (l, j) in traj:
                cs |= traj
                break
            if (l, j) in cs:
                break
            if (l, j) in ts:
                c += 1
                break
            traj.add((l, j))
    return c # Chai Wah Wu, Aug 03 2017

Crossrefs

Cf. A284116, A284119, A284121, A289670, A289671, A289672, A289673, A289674, A289675, A289677.

Cf. also A290436-A290441.

Sequence in context: A023191 A220188 A238551 * A238189 A029256 A216501

Adjacent sequences: A289673 A289674 A289675 * A289677 A289678 A289679

Keyword

nonn

Author

N. J. A. Sloane, Aug 01 2017; corrected by Don Reble, Aug 01 2017 (there were errors in A289670).

Status

approved