A245582 Number of binary strings of length n having a cyclic shift that is a palindrome.

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

Offset

0,2

Comments

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

Apparently A045655 is a bisection. - R. J. Mathar, Mar 11 2017

Links

Table of n, a(n) for n=0..37.

Lars Blomberg, C# program for generating the sequence.

Example

For n = 4 the function counts the strings 0000, 0011, 0110 and their bitwise complements.

Mathematica

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 *)

Crossrefs

Sequence in context: A285114 A071418 A353268 * A361790 A197820 A064862

Adjacent sequences: A245579 A245580 A245581 * A245583 A245584 A245585

Keyword

nonn

Author

Jeffrey Shallit, Jul 26 2014

Extensions

a(25)-a(37) from Lars Blomberg, Oct 20 2014

Status

approved