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 A087432 #22 Aug 23 2017 11:15:53
%S A087432 1,1,3,7,19,51,143,407,1179,3451,10183,30207,89939,268451,802623,
%T A087432 2402407,7196299,21567051,64657463,193885007,581480259,1744091251,
%U A087432 5231574703,15693326007,47077181819,141225953051,423666674343
%N A087432 Expansion of 1+x*(1-x-4*x^2)/((1+x)*(1-2*x)*(1-3*x)).
%C A087432 Binomial transform of A047849 (with interpolated zeros, 1,0,2,0,6,0,...). Binomial transform is A087433.
%H A087432 Harvey P. Dale, <a href="/A087432/b087432.txt">Table of n, a(n) for n = 0..1000</a>
%H A087432 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-1,-6).
%F A087432 a(n) = (-1)^n/6+2^n/3+3^n/6, n>0.
%F A087432 For n>4, a(n) = 6*a(n-1) - 9*a(n-2) - 4*a(n-3) + 12*a(n-4). - _Gary W. Adamson_, Jun 14 2006
%t A087432 CoefficientList[Series[1+x (1-x-4x^2)/((1+x)(1-2x)(1-3x)),{x,0,30}],x] (* or *) LinearRecurrence[{4,-1,-6},{1,1,3,7},30] (* _Harvey P. Dale_, Aug 23 2017 *)
%o A087432 (PARI) Vec((x-1)*(2*x^2+2*x-1)/((1+x)*(1-2*x)*(1-3*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012, corrected Nov 27 2014
%Y A087432 First differences of A093379.
%K A087432 nonn,easy
%O A087432 0,3
%A A087432 _Paul Barry_, Sep 02 2003