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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. 2
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.

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]

CROSSREFS

Cf. A237500, A237501.

Sequence in context: A266074 A191822 A238549 * A279726 A137848 A182629

Adjacent sequences:  A237499 A237500 A237501 * A237503 A237504 A237505

KEYWORD

nonn

AUTHOR

Giovanni Resta, Feb 08 2014

STATUS

approved

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Last modified December 10 20:55 EST 2018. Contains 318049 sequences. (Running on oeis4.)