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%I #26 Sep 23 2021 01:27:18
%S 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,
%T 116,250,231,210,462,459,438,960,990,966,2069,2114,2089,4296,4237,
%U 4155,8485,8234,8032,16496,16054,15657,32041,31280,30325,61700,60252,58379,118357,115810,112885
%N a(n) = A289670(n)/2^f(n), where f(n) = 2*floor((n-1)/3) + ((n+2) mod 3).
%C 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.
%o (Python)
%o from __future__ import division
%o def A289676(n):
%o c, k, r, n2, cs, ts = 0, 1+(n-1)//3, 2**((n-1) % 3), 2**(n-1), set(), set()
%o for i in range(2**k):
%o j, l = int(bin(i)[2:],8)*r, n2
%o traj = set([(l,j)])
%o while True:
%o if j >= l:
%o j = j*16+13
%o l *= 2
%o else:
%o j *= 4
%o l //= 2
%o if l == 0:
%o c += 1
%o ts |= traj
%o break
%o j %= 2*l
%o if (l,j) in traj:
%o cs |= traj
%o break
%o if (l,j) in cs:
%o break
%o if (l,j) in ts:
%o c += 1
%o break
%o traj.add((l,j))
%o return c # _Chai Wah Wu_, Aug 03 2017
%Y Cf. A284116, A284119, A284121, A289670, A289671, A289672, A289673, A289674, A289675, A289677.
%Y Cf. also A290436-A290441.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Aug 01 2017; corrected by _Don Reble_, Aug 01 2017 (there were errors in A289670).
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