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 A056488 #41 Sep 08 2022 08:45:01
%S A056488 6,21,36,126,216,756,1296,4536,7776,27216,46656,163296,279936,979776,
%T A056488 1679616,5878656,10077696,35271936,60466176,211631616,362797056,
%U A056488 1269789696,2176782336,7618738176,13060694016,45712429056,78364164096,274274574336,470184984576
%N A056488 Number of periodic palindromes using a maximum of six different symbols.
%C A056488 Also number of necklaces with n beads and 6 colors that are the same when turned over and hence have reflection symmetry. - _Herbert Kociemba_, Nov 24 2016
%D A056488 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 A056488 Vincenzo Librandi, <a href="/A056488/b056488.txt">Table of n, a(n) for n = 1..1000</a>
%H A056488 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,6).
%F A056488 a(n) = 6^((n+1)/2) for n odd, a(n) = 6^(n/2)*7/2 for n even.
%F A056488 From _Colin Barker_, Jul 08 2012: (Start)
%F A056488 a(n) = 6*a(n-2).
%F A056488 G.f.: 3*x*(2+7*x)/(1-6*x^2). (End)
%F A056488 a(n) = (k^floor((n+1)/2) + k^ceiling((n+1)/2)) / 2, where k = 6 is the number of possible colors. - _Robert A. Russell_, Sep 22 2018
%e A056488 G.f. = 6*x + 21*x^2 + 36*x^3 + 126*x^4 + 216*x^5 + 756*x^6 + 1296*x^7 + ...
%e A056488 For example, aaabbb is not a (finite) palindrome but it is a periodic palindrome.
%t A056488 LinearRecurrence[{0,6},{6,21},30] (* _Harvey P. Dale_, Feb 02 2015 *)
%t A056488 k = 6; Table[(k^Floor[(n + 1)/2] + k^Ceiling[(n + 1)/2]) / 2, {n, 30}] (* _Robert A. Russell_, Sep 21 2018 *)
%t A056488 If[EvenQ[#], 6^(# / 2) 7/2, 6^((# + 1) / 2)]&/@Range[30] (* _Vincenzo Librandi_, Sep 22 2018 *)
%o A056488 (PARI) a(n) = if(n%2, 6^((n+1)/2), 7*6^(n/2)/2); \\ _Altug Alkan_, Sep 21 2018
%o A056488 (Magma) [IsEven(n) select 6^(n div 2)*7/2 else 6^((n+1) div 2): n in [1..30]]; // _Vincenzo Librandi_, Sep 22 2018
%Y A056488 Column 6 of A284855.
%Y A056488 Cf. A029744, A038754, A056452.
%K A056488 nonn,easy
%O A056488 1,1
%A A056488 _Marks R. Nester_
%E A056488 More terms from _Vincenzo Librandi_, Sep 22 2018