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 A091003 #19 Dec 14 2024 03:59:16
%S A091003 1,-1,4,-10,34,-94,298,-862,2650,-7822,23722,-70654,212986,-636910,
%T A091003 1914826,-5736286,17225242,-51642958,154994410,-464852158,1394818618,
%U A091003 -4183931566,12552843274,-37656432670,112973492314,-338912088334,1016753042218
%N A091003 Expansion of (1-3*x^2)/((1-2*x)*(1+3*x)).
%C A091003 Inverse binomial transform of A091000.
%H A091003 G. C. Greubel, <a href="/A091003/b091003.txt">Table of n, a(n) for n = 0..1000</a>
%H A091003 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-1,6).
%F A091003 2^n = A091003(n) + 3*A091004(n) + 6*A091005(n).
%F A091003 a(n) = (2^n + 4*(-3)^n + 5*0^n)/10.
%F A091003 E.g.f.: (exp(2*x) + 4*exp(-3*x) + 5)/10. - _G. C. Greubel_, Feb 01 2019
%t A091003 CoefficientList[Series[(1-3x^2)/((1-2x)(1+3x)),{x,0,30}],x] (* _Harvey P. Dale_, Dec 23 2014 *)
%t A091003 Join[{1}, LinearRecurrence[{-1,6}, {-1,4}, 30]] (* _G. C. Greubel_, Feb 01 2019 *)
%o A091003 (PARI) vector(30, n, n--; (2^n + 4*(-3)^n + 5*0^n)/10) \\ _G. C. Greubel_, Feb 01 2019
%o A091003 (Magma) [1] cat [(2^n + 4*(-3)^n)/10: n in [1..30]]; // _G. C. Greubel_, Feb 01 2019
%o A091003 (Sage) [1] + [(2^n + 4*(-3)^n)/10 for n in (1..30)] # _G. C. Greubel_, Feb 01 2019
%o A091003 (GAP) Concatenation([1], List([1..30], n -> (2^n + 4*(-3)^n)/10)); # _G. C. Greubel_, Feb 01 2019
%K A091003 easy,sign
%O A091003 0,3
%A A091003 _Paul Barry_, Dec 13 2003