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 A237502 Number of binary strings of length 2n which contain the ones' complements and the reversals of each of their two halves. 3
 2, 6, 8, 16, 26, 46, 72, 116, 184, 288, 434, 646, 980, 1444, 2122, 3066, 4500, 6452, 9362, 13294 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..20. Michael S. Branicky, Python program EXAMPLE The two halves of 1000111000 are 10001 and 11000. Their reversals are 10001 and 00011, and their complements are 01110 and 00111 and all are substrings of 1000111000. Since there are 25 other strings of length 2*5 with this property, a(5) = 26. MATHEMATICA sQ[L_, {s__}] := MatchQ[L, {___, s, ___}]; a[n_] := Length@ Select[ Tuples[{0, 1}, 2*n], sQ[#, Reverse[Take[#, n]]] && sQ[#, Reverse[Take[#, -n ]]] && sQ[#, 1 - Take[#, n]] && sQ[#, 1 - Take[#, -n]] &]; Array[a, 8] PROG (Python) # see link for faster version from itertools import product as prod def comp(s): z, o = ord('0'), ord('1'); return s.translate({z:o, o:z}) def ok(s): a, b = s[len(s)//2:], s[:len(s)//2] return comp(a) in s and comp(b) in s and a[::-1] in s and b[::-1] in s def a(n): return 2*sum(ok("0"+"".join(p)) for p in prod("01", repeat=2*n-1)) print([a(n) for n in range(1, 12)]) # Michael S. Branicky, Feb 06 2021 CROSSREFS Cf. A237500, A237501. Sequence in context: A266074 A191822 A238549 * A279726 A337881 A331974 Adjacent sequences: A237499 A237500 A237501 * A237503 A237504 A237505 KEYWORD nonn,more AUTHOR Giovanni Resta, Feb 08 2014 STATUS approved

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Last modified May 29 08:30 EDT 2023. Contains 363029 sequences. (Running on oeis4.)