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 A102129 #23 Mar 09 2024 14:54:20
%S A102129 1,4,15,66,277,1176,4979,21094,89353,378508,1603383,6792042,28771549,
%T A102129 121878240,516284507,2187016270,9264349585,39244414612,166242008031,
%U A102129 704212446738,2983091794981,12636579626664,53529410301635,226754220833206,960546293634457
%N A102129 Expansion of (1 - x)*(1 + 2*x) / ((1 + x)*(1 - 4*x - x^2)).
%C A102129 A floretion-generated, Pellian related sequence.
%C A102129 Floretion Algebra Multiplication Program, FAMP Code: 2ibaseiforseq[A*B] with A = - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki' B = - .5'ii' + .5'jj' + .5'kk' + .5e, 1vesforseq(n) = (-1)^n, 2basekforseq[A*B] = A048875, ForType: 1A
%C A102129 Sequence results from a force transform of the periodic sequence with initial period (1, -1).
%H A102129 Colin Barker, <a href="/A102129/b102129.txt">Table of n, a(n) for n = 0..1000</a>
%H A102129 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,5,1).
%F A102129 a(n) + a(n+1) = A048875(n+1) - A048875(n).
%F A102129 a(n) = -(10*(-1)^n + (2-sqrt(5))^n*(-15+sqrt(5)) - (2+sqrt(5))^n*(15+sqrt(5))) / 20. - _Colin Barker_, Jun 06 2017
%t A102129 CoefficientList[ Series[((-1 + x)(2x + 1))/((1 + x)(x^2 + 4x - 1)), {x, 0, 22}], x] (* _Robert G. Wilson v_, Mar 16 2005 *)
%o A102129 (PARI) Vec((1 - x)*(1 + 2*x) / ((1 + x)*(1 - 4*x - x^2)) + O(x^30)) \\ _Colin Barker_, Jun 06 2017
%Y A102129 Cf. A048875.
%K A102129 easy,nonn
%O A102129 0,2
%A A102129 _Creighton Dement_, Mar 15 2005
%E A102129 Corrected and extended by _Robert G. Wilson v_, Mar 16 2005