This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A245582 #29 Mar 11 2017 14:46:50
%S A245582 1,2,2,8,6,32,20,100,54,260,152,684,348,1640,884,3728,1974,8672,4556,
%T A245582 19420,10056,42736,22508,94164,48636,204632,106472,441764,228444,
%U A245582 950216,491120,2031556,1046454,4323888,2228192,9174400,4713252,19398584
%N A245582 Number of binary strings of length n having a cyclic shift that is a palindrome.
%C A245582 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
%C A245582 Apparently A045655 is a bisection. - _R. J. Mathar_, Mar 11 2017
%H A245582 Lars Blomberg, <a href="/A245582/a245582.txt">C# program for generating the sequence.</a>
%e A245582 For n = 4 the function counts the strings 0000, 0011, 0110 and their bitwise complements.
%t A245582 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 *)
%K A245582 nonn
%O A245582 0,2
%A A245582 _Jeffrey Shallit_, Jul 26 2014
%E A245582 a(25)-a(37) from _Lars Blomberg_, Oct 20 2014