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 A078058 #22 Mar 19 2025 09:55:36
%S A078058 1,-3,7,-18,46,-117,298,-759,1933,-4923,12538,-31932,81325,-207120,
%T A078058 527497,-1343439,3421495,-8713926,22192786,-56520993,143948698,
%U A078058 -366611175,933692041,-2377943955,6056191126,-15424018248,39282171577,-100044552528,254795294881,-648917313867
%N A078058 Expansion of (1-x)/(1+2*x-x^2+x^3).
%C A078058 a(n) is the upper left entry of the n-th power of the 3 X 3 matrix M = [-3, -3, 1; 1, 1, 0; 1, 0, 0]; a(n) = M^n [1, 1]. - _Philippe Deléham_, Apr 19 2023
%H A078058 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-2,1,-1).
%F A078058 a(n) = -2*a(n-1) + a(n-2) - a(n-3) for n > 2; a(0) = 1, a(1) = -3, a(2) = 7. - _Harvey P. Dale_, Oct 22 2011
%F A078058 a(n) = Sum_{k = 0..n} A188316(n, k)*(-3)^k. - _Philippe Deléham_, Apr 19 2023
%F A078058 a(n) = A077986(n)-A077986(n-1) . - _R. J. Mathar_, Mar 19 2025
%t A078058 CoefficientList[Series[(1-x)/(1+2x-x^2+x^3),{x,0,30}],x] (* or *) LinearRecurrence[{-2,1,-1},{1,-3,7},31] (* _Harvey P. Dale_, Oct 22 2011 *)
%o A078058 (PARI) Vec((1-x)/(1+2*x-x^2+x^3)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 27 2012
%K A078058 sign,easy
%O A078058 0,2
%A A078058 _N. J. A. Sloane_, Nov 17 2002