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A289676 a(n) = A289670(n)/2^f(n), where f(n) = 2*floor((n-1)/3)+((n+2) mod 3). 6
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 (list; graph; refs; listen; history; text; internal format)
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 affect 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

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Last modified September 30 22:26 EDT 2020. Contains 337440 sequences. (Running on oeis4.)