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 A096252 #24 Feb 15 2024 12:12:40
%S A096252 4,-4,8,-32,-32,-64,-256,256,-512,2048,2048,4096,16384,-16384,32768,
%T A096252 -131072,-131072,-262144,-1048576,1048576,-2097152,8388608,8388608,
%U A096252 16777216,67108864,-67108864,134217728,-536870912,-536870912,-1073741824
%N A096252 Array read by rows, starting with n=0: row n lists A057077(n+1)*8^(n+1)/2, A057077(n+2)*8^(n+1)/2, A057077(n+1)*8^(n+1).
%C A096252 a(n) = ves( ('i + 'ii' + 'ij' + 'ik')^n ) a(n) = ves( ('j + 'jj' + 'ji' + 'jk')^n ) a(n) = ves( ('k + 'kk' + 'ki' + 'kj')^n ).
%C A096252 The elements x = 'i + 'ii' + 'ij' + 'ik'; y = 'j + 'jj' + 'ji' + 'jk'; and z = 'k + 'kk' + 'ki' + 'kj' are elements of the ring generated from the quaternion factor space Q X Q / {(1,1), (-1,-1)}. Each is represented by a gray shaded area of "Floret's cube". The elements x/2, y/2, z/2 are members of a group, itself a subset of the real algebra generated from Q X Q / {(1,1), (-1,-1)}, which is isomorphic to Q X C_3 (order 24).
%C A096252 This sequence is the term-wise sum of three sequences: a(n) = ves(x^n) = jes(x^n) + les(x^n) + tes(x^n), where jes(x^n)=(1, -6, 8, -24, 16, 0, -64, 384, -512, 1536, -1024, 0, 4096, -24576, 32768, -98304, ...), les(x^n)=(3, 0, 0, 0, -48, 0 -192, 0, 0, 0, 3072, 0, 12288, 0, 0, 0, ...), tes(x^n)=(0, 2, 0, -8, 0, -64, 0, -128, 0, 512, 0, 4096, 0, 8192, 0, -32768, ...). Concerning "les"- notice that if (..., s, 0, 0, 0, t, ...), then t = -16s and if (..., s, 0, t, ...), then t = 4s.
%H A096252 Danny Rorabaugh, <a href="/A096252/b096252.txt">Table of n, a(n) for n = 0..1000</a>
%H A096252 C. Dement, <a href="http://mathforum.org/discuss/sci.math/t/622432">The Math Forum</a>.
%H A096252 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-16).
%F A096252 a(n)= 4*a(n-2)-16*a(n-4). G.f.: 4*(1-x-2*x^2-4*x^3)/(1-4*x^2+16*x^4). - _R. J. Mathar_, Nov 26 2008
%F A096252 a(n) = (-1)^(floor((floor(n/3)+((n mod 3) mod 2)+1)/2)) * 8^(floor(n/3)+1) / 2^(((n+1)^2) mod 3). - _Danny Rorabaugh_, May 13 2016
%F A096252 a(n) = 4*(-1)^floor((n+1)/2)*A138230(n). - _R. J. Mathar_, May 21 2019
%t A096252 CoefficientList[Series[4(1-x-2x^2-4x^3)/(1-4x^2+16x^4),{x,0,40}],x] (* or *) LinearRecurrence[ {0,4,0,-16},{4,-4,8,-32},40] (* _Harvey P. Dale_, Feb 15 2024 *)
%o A096252 (Sage)
%o A096252 [(-1)^(floor((floor(n/3)+((n%3)%2)+1)/2)) * 8^(floor(n/3)+1) / 2^(((n+1)^2)%3) for n in range(30)]
%o A096252 # _Danny Rorabaugh_, May 13 2016
%Y A096252 Cf. A048473, A094015.
%K A096252 sign,easy
%O A096252 0,1
%A A096252 _Creighton Dement_, Jul 31 2004
%E A096252 Edited with clearer definition by _Omar E. Pol_, Dec 29 2008