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 A056490 #41 Sep 08 2022 08:45:01
%S A056490 0,0,0,0,0,12,24,132,240,900,1560,4980,8400,24612,40824,113652,186480,
%T A056490 502500,818520,2158260,3498000,9087012,14676024,37728372,60780720,
%U A056490 155091300,249401880,632972340,1016542800,2569858212,4123173624,10393634292,16664094960
%N A056490 Number of periodic palindromes using exactly four different symbols.
%D A056490 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 A056490 Muniru A Asiru, <a href="/A056490/b056490.txt">Table of n, a(n) for n = 1..700</a>
%H A056490 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,9,-9,-26,26,24,-24).
%F A056490 a(n) = 2*A056344(n) - A056284(n).
%F A056490 G.f.: 12*x^6*(1+x)/((1-x)*(1-2*x)*(1+2*x)*(1-2*x^2)*(1-3*x^2)). - _Colin Barker_, May 06 2012
%F A056490 a(n) = (k!/2)*(S2(floor((n+1)/2),k) + S2(ceiling((n+1)/2),k)), with k=4 different colors used and where S2(n,k) is the Stirling subset number A008277. - _Robert A. Russell_, Jun 05 2018
%e A056490 For example, aaabbb is not a (finite) palindrome but it is a periodic palindrome.
%e A056490 For n=6, the 12 arrangements are ABACDC, ABADCD, ACABDB, ACADBD, ADABCB, ADACBC, ABCDCB, ABDCDB, ACBDBC, ACDBDC, ADBCBD, and ADCBCD.
%p A056490 a:=n->(factorial(4)/2)*(Stirling2(floor((n+1)/2),4)+Stirling2(ceil((n+1)/2),4)): seq(a(n),n=1..35); # _Muniru A Asiru_, Sep 26 2018
%t A056490 k = 4; Table[(k!/2) (StirlingS2[Floor[(n + 1)/2], k] +
%t A056490 StirlingS2[Ceiling[(n + 1)/2], k]), {n, 1, 40}] (* _Robert A. Russell_, Jun 05 2018 *)
%t A056490 LinearRecurrence[{1,9,-9,-26,26,24,-24}, {0,0,0,0,0,12,24}, 40] (* _Robert A. Russell_, Sep 29 2018 *)
%o A056490 (PARI) a(n) = my(k=4); (k!/2)*(stirling(floor((n+1)/2), k, 2) + stirling(ceil((n+1)/2), k, 2)); \\ _Michel Marcus_, Jun 05 2018
%o A056490 (GAP) a:=[0,0,0,0,0,12,24];; for n in [8..35] do a[n]:=a[n-1]+9*a[n-2]-9*a[n-3]-26*a[n-4]+26*a[n-5]+24*a[n-6]-24*a[n-7]; od; a; # _Muniru A Asiru_, Sep 26 2018
%o A056490 (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); [0, 0, 0, 0, 0] cat Coefficients(R!(12*x^6*(1+x)/((1-x)*(1-2*x)*(1+2*x)*(1-2*x^2)*(1-3*x^2)))); // _G. C. Greubel_, Oct 13 2018
%Y A056490 Cf. A056284, A056344, A056455.
%Y A056490 Column 4 of A305540.
%K A056490 nonn,easy
%O A056490 1,6
%A A056490 _Marks R. Nester_