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 A237501 Number of binary strings of length 2n which contain the reversals of each of their two halves. 3
 4, 12, 42, 106, 300, 654, 1664, 3300, 7940, 15018, 34948, 64396, 147130, 267404, 604722, 1090998, 2453492, 4409000, 9886266, 17729222 (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 01111011 are 0111 and 1011. Their reversals are 1110 and 1101, and both are substrings of 01111011. Since there are 105 other strings of length 2*4 with this property, a(4) = 106. MATHEMATICA sQ[L_, {s__}] := MatchQ[L, {___, s, ___}]; a[n_] := Length@ Select[ Tuples[{0, 1}, 2*n], sQ[#, Reverse[Take[#, n]]] && sQ[#, Reverse[Take[#, -n ]]] &]; Array[a, 8] PROG (Python) # see link for faster version from itertools import product as prod def ok(s): return s[:len(s)//2][::-1] in s and s[len(s)//2:][::-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, A237502. Sequence in context: A242470 A242471 A239800 * A300124 A343517 A308371 Adjacent sequences: A237498 A237499 A237500 * A237502 A237503 A237504 KEYWORD nonn,more AUTHOR Giovanni Resta, Feb 08 2014 EXTENSIONS a(17)-a(20) from Michael S. Branicky, Feb 06 2021 STATUS approved

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Last modified May 30 03:43 EDT 2023. Contains 363044 sequences. (Running on oeis4.)