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 A056503 #28 Sep 20 2018 03:26:40
%S A056503 1,2,2,4,4,7,8,14,16,26,32,51,64,100,128,198,256,392,512,778,1024,
%T A056503 1552,2048,3091,4096,6176,8192,12324,16384,24640,32768,49222,65536,
%U A056503 98432,131072,196744,262144,393472,524288,786698,1048576,1573376,2097152,3146256,4194304
%N A056503 Number of periodic palindromic structures of length n using a maximum of two different symbols.
%C A056503 For example, aaabbb is not a (finite) palindrome but it is a periodic palindrome. Permuting the symbols will not change the structure.
%C A056503 A periodic palindrome is just a necklace that is equivalent to its reverse. The number of binary periodic palindromes of length n is given by A164090(n). A binary periodic palindrome can only be equivalent to its complement when there are an equal number of 0's and 1's. - _Andrew Howroyd_, Sep 29 2017
%C A056503 Number of cyclic compositions (necklaces of positive integers) summing to n that can be rotated to form a palindrome. - _Gus Wiseman_, Sep 16 2018
%D A056503 M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
%H A056503 Andrew Howroyd, <a href="/A056503/b056503.txt">Table of n, a(n) for n = 1..200</a>
%F A056503 a(2n+1) = A164090(2n+1)/2 = 2^n, a(2n) = (A164090(2n) + A045674(n))/2. - _Andrew Howroyd_, Sep 29 2017
%e A056503 From _Gus Wiseman_, Sep 16 2018: (Start)
%e A056503 The sequence of palindromic cyclic compositions begins:
%e A056503 (1) (2) (3) (4) (5) (6) (7)
%e A056503 (11) (111) (22) (113) (33) (115)
%e A056503 (112) (122) (114) (133)
%e A056503 (1111) (11111) (222) (223)
%e A056503 (1122) (11113)
%e A056503 (11112) (11212)
%e A056503 (111111) (11122)
%e A056503 (1111111)
%e A056503 (End)
%t A056503 (* b = A164090, c = A045674 *)
%t A056503 b[n_] := (1/4)*(7 - (-1)^n)*2^((1/4)*(2*n + (-1)^n - 1));
%t A056503 c[0] = 1; c[n_] := c[n] = If[EvenQ[n], 2^(n/2-1) + c[n/2], 2^((n-1)/2)];
%t A056503 a[n_?OddQ] := b[n]/2; a[n_?EvenQ] := (1/2)*(b[n] + c[n/2]);
%t A056503 Array[a, 45] (* _Jean-François Alcover_, Oct 08 2017, after _Andrew Howroyd_ *)
%t A056503 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],Function[q,And[Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And],Array[SameQ[RotateRight[q,#],Reverse[RotateRight[q,#]]]&,Length[q],1,Or]]]]],{n,15}] (* _Gus Wiseman_, Sep 16 2018 *)
%Y A056503 Row sums of A179181.
%Y A056503 Cf. A016116, A045674, A056508, A164090, A285012.
%Y A056503 Cf. A000740, A000837, A008965, A025065, A059966, A242414, A296302, A317085, A317086, A317087, A318731.
%K A056503 nonn
%O A056503 1,2
%A A056503 _Marks R. Nester_
%E A056503 a(17)-a(45) from _Andrew Howroyd_, Apr 07 2017