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A245582
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Number of binary strings of length n having a cyclic shift that is a palindrome.
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1
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1, 2, 2, 8, 6, 32, 20, 100, 54, 260, 152, 684, 348, 1640, 884, 3728, 1974, 8672, 4556, 19420, 10056, 42736, 22508, 94164, 48636, 204632, 106472, 441764, 228444, 950216, 491120, 2031556, 1046454, 4323888, 2228192, 9174400, 4713252, 19398584
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OFFSET
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0,2
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COMMENTS
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Alternatively (Luke Schaeffer), those binary strings of length n that can be written as the concatenation of two palindromes, one of which has even length. - Jeffrey Shallit, Jan 28 2016
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LINKS
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EXAMPLE
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For n = 4 the function counts the strings 0000, 0011, 0110 and their bitwise complements.
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MATHEMATICA
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palQ[lst_] := lst==Reverse[lst]; a[n_] := (For[k=0; cnt=0, k<2^n, k++, bb = PadLeft[IntegerDigits[k, 2], n]; If[MatchQ[bb, {a___ /; palQ[{a}], b___ /; palQ[{b}]} /; EvenQ[Length[{a}]] || EvenQ[Length[{b}]]], cnt++]]; cnt); Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 25}] (* Jean-François Alcover, Jan 28 2016 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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