A237500 Number of binary strings of length 2n which contain the ones' complement of each of their two halves.

2, 6, 12, 28, 58, 118, 244, 500, 1004, 2024, 4070, 8150, 16340, 32720, 65450, 130986, 262056, 524136, 1048422, 2096982, 4194000, 8388300, 16776906

Offset

1,1

Links

Table of n, a(n) for n=1..23.

Michael S. Branicky, Python program

Example

The two halves of 011001 are 011 and 001. Their complements are 100 and 110, and both are substrings of 011001. Since there are 11 other strings of length 2*3 with this property, a(3) = 12.

Mathematica

sQ[L_, {s__}] := MatchQ[L, {___, s, ___}]; a[n_] := Length@ Select[ Tuples[{0, 1}, 2@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): return comp(s[:len(s)//2]) in s and comp(s[len(s)//2:]) 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. A237501, A237502.

Sequence in context: A089820 A122746 A191394 * A330455 A183467 A057582

Adjacent sequences: A237497 A237498 A237499 * A237501 A237502 A237503

Keyword

nonn,more

Author

Giovanni Resta, Feb 08 2014

Extensions

a(17)-a(21) from Michael S. Branicky, Feb 06 2021

a(22) from Michael S. Branicky, Jul 06 2022

a(23) from Michael S. Branicky, Jul 25 2022

Status

approved