

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
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OFFSET

1,1


LINKS



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*n1))


CROSSREFS



KEYWORD

nonn,more


AUTHOR



STATUS

approved



