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 A292521 #16 Sep 19 2017 03:24:56
%S A292521 2,0,1,-1,3,-3,6,-10,15,-25,41,-65,106,-172,277,-449,727,-1175,1902,
%T A292521 -3078,4979,-8057,13037,-21093,34130,-55224,89353,-144577,233931,
%U A292521 -378507,612438,-990946,1603383,-2594329,4197713,-6792041,10989754,-17781796,28771549,-46553345
%N A292521 a(n) = a(n-2) - 2a(n-3) + a(n-4) for n>3, with a(0)=2, a(1)=0, a(2)=1, a(3)=-1, a sequence related to Pellian numbers.
%C A292521 Successive differences begin:
%C A292521 2, 0, 1, -1, 3, -3, 6, -10, 15, -25, ... = a(n)
%C A292521 -2, 1, -2, 4, -6, 9, -16, 25, -40, 66, ... = b(n)
%C A292521 3, -3, 6, -10, 15, -25, 41, -65, 106, -172, ... = a(n+4)
%C A292521 -6, 9, -16, 25, -40, 66, -106, 171, -278, 449, ... = b(n+4)
%C A292521 15, -25, 41, -65, 106, -172, 277, -449, 727, -1175, ... = a(n+8)
%C A292521 ...
%C A292521 Main diagonal [2] 1, 6, 25, 106, 449, ... (omitting first term) is A048875 (Pellian numbers with second term 6).
%H A292521 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,-2,1).
%F A292521 G.f.: (2 - x^2 + 3*x^3) / (1 - x^2 + 2*x^3 - x^4).
%F A292521 a(n) = A291660(-n) (negative indices computed using A291660 sequence function).
%F A292521 a(n) = (1/15)*2^(n-1)*((9*sqrt(5)+30)/(1+sqrt(5))^n + (30-9*sqrt(5))/(1- sqrt(5))^n - 5*sqrt(3)*2^(1-n)*sin(n*Pi/3)).
%t A292521 LinearRecurrence[{0, 1, -2, 1}, {2, 0, 1, -1}, 40]
%o A292521 (PARI) x='x+O('x^99); Vec((2-x^2+3*x^3)/(1-x^2+2*x^3-x^4)) \\ _Altug Alkan_, Sep 18 2017
%Y A292521 Cf. A048875, A291660.
%K A292521 sign
%O A292521 0,1
%A A292521 _Jean-François Alcover_ and _Paul Curtz_, Sep 18 2017