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 A128416 #19 Mar 09 2022 03:31:39 %S A128416 1,-4,9,-24,69,-204,609,-1824,5469,-16404,49209,-147624,442869, %T A128416 -1328604,3985809,-11957424,35872269,-107616804,322850409,-968551224, %U A128416 2905653669,-8716961004,26150883009,-78452649024,235357947069,-706073841204,2118221523609 %N A128416 Expansion of (1-4x^2)/(1+4x+3x^2). %C A128416 Diagonal sums of number triangle A128414. %H A128416 Colin Barker, <a href="/A128416/b128416.txt">Table of n, a(n) for n = 0..1000</a> %H A128416 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-4,-3). %F A128416 G.f.: (1-4*x^2)/(1+4*x+3*x^2). %F A128416 For n > 1, |a(n)| = 3*(|a(n-1)| - 1). - Tamas Kalmar-Nagy (integers(AT)kalmarnagy.com), Sep 17 2010 %F A128416 From _Colin Barker_, Sep 21 2016: (Start) %F A128416 a(n) = (-1)^n*(9+5*3^n)/6 for n>0. %F A128416 a(n) = -4*a(n-1)-3*a(n-2) for n>2. (End) %o A128416 (PARI) Vec((1-4*x^2)/(1+4*x+3*x^2) + O(x^30)) \\ _Colin Barker_, Sep 21 2016 %Y A128416 Cf. A128414. %K A128416 easy,sign %O A128416 0,2 %A A128416 _Paul Barry_, Mar 02 2007