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 A087463 #15 Nov 04 2015 11:56:07
%S A087463 0,1,1,0,5,11,0,43,85,0,341,683,0,2731,5461,0,21845,43691,0,174763,
%T A087463 349525,0,1398101,2796203,0,11184811,22369621,0,89478485,178956971,0,
%U A087463 715827883,1431655765,0,5726623061,11453246123,0,45812984491,91625968981,0
%N A087463 Generalized multiplicative Jacobsthal sequence.
%C A087463 Set A001045(3n)=0 in A001045.
%C A087463 2^n = A087462(n) + a(n) + A087464(n) provides a decomposition of Pascal's triangle.
%H A087463 Colin Barker, <a href="/A087463/b087463.txt">Table of n, a(n) for n = 0..1000</a>
%H A087463 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,7,0,0,8).
%F A087463 a(n) = Sum_{k=0..n} if (mod(n*k, 3)=1, 1, 0)*C(n, k).
%F A087463 a(n) = (2/9)*(1-cos(2*Pi*n/3))*(2^n-(-1)^n).
%F A087463 From _Colin Barker_, Nov 02 2015: (Start)
%F A087463 a(n) = 7*a(n-3)+8*a(n-6) for n>5.
%F A087463 G.f.: -x*(4*x^4-2*x^3+x+1) / ((x+1)*(2*x-1)*(x^2-x+1)*(4*x^2+2*x+1)).
%F A087463 (End)
%o A087463 (PARI) concat(0, Vec(-x*(4*x^4-2*x^3+x+1)/((x+1)*(2*x-1)*(x^2-x+1)*(4*x^2+2*x+1)) + O(x^100))) \\ _Colin Barker_, Nov 02 2015
%K A087463 easy,nonn
%O A087463 0,5
%A A087463 _Paul Barry_, Sep 08 2003