cp's OEIS Frontend

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

%I A289676 #28 Jul 09 2025 04:19:54
%S A289676 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 A289676 116,250,231,210,462,459,438,960,990,966,2069,2114,2089,4296,4237,
%U A289676 4155,8485,8234,8032,16496,16054,15657,32041,31280,30325,61700,60252,58379,118357,115810,112885
%N A289676 a(n) = A289670(n)/2^f(n), where f(n) = 2*floor((n-1)/3) + ((n+2) mod 3).
%C A289676 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 A289676 (Python)
%o A289676 from __future__ import division
%o A289676 def A289676(n):
%o A289676     c, k, r, n2, cs, ts = 0, 1+(n-1)//3, 2**((n-1) % 3), 2**(n-1), set(), set()
%o A289676     for i in range(2**k):
%o A289676         j, l = int(bin(i)[2:],8)*r, n2
%o A289676         traj = set([(l,j)])
%o A289676         while True:
%o A289676             if j >= l:
%o A289676                 j = j*16+13
%o A289676                 l *= 2
%o A289676             else:
%o A289676                 j *= 4
%o A289676                 l //= 2
%o A289676             if l == 0:
%o A289676                 c += 1
%o A289676                 ts |= traj
%o A289676                 break
%o A289676             j %= 2*l
%o A289676             if (l,j) in traj:
%o A289676                 cs |= traj
%o A289676                 break
%o A289676             if (l,j) in cs:
%o A289676                 break
%o A289676             if (l,j) in ts:
%o A289676                 c += 1
%o A289676                 break
%o A289676             traj.add((l,j))
%o A289676     return c # _Chai Wah Wu_, Aug 03 2017
%Y A289676 Cf. A284116, A284119, A284121, A289670, A289671, A289672, A289673, A289674, A289675, A289677.
%Y A289676 Cf. also A290436-A290441.
%K A289676 nonn
%O A289676 1,1
%A A289676 _N. J. A. Sloane_, Aug 01 2017
%E A289676 Corrected by _Don Reble_, Aug 01 2017 (there were errors in A289670)