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 A094567 #27 Mar 05 2016 16:17:44
%S A094567 1,4,30,203,1394,9552,65473,448756,3075822,21081995,144498146,
%T A094567 990405024,6788337025,46527954148,318907342014,2185823439947,
%U A094567 14981856737618,102687173723376,703828359326017,4824111341558740,33064951031585166,226630545879537419
%N A094567 Associated with alternating row sums of array in A094566.
%H A094567 Colin Barker, <a href="/A094567/b094567.txt">Table of n, a(n) for n = 0..1000</a>
%H A094567 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,6,-1).
%F A094567 a(n) = F(4n+1) - a(n-1) for n >= 1, with a(0) = 1.
%F A094567 a(n) = (Fib(4n+3) + (-1)^n)/3. - _Ralf Stephan_, Dec 04 2004
%F A094567 a(n) = 6*a(n-1)+6*a(n-2)-a(n-3), with a(0)=1, a(1)=4, a(2)=30. - _Harvey P. Dale_, Jul 13 2011
%F A094567 G.f.: (1-2*x)/(1-6*x-6*x^2+x^3). - _Harvey P. Dale_, Jul 13 2011
%F A094567 a(n) = (-1)^n*sum((-1)^k*Fibonacci(4*k+1), k=0..n). - _Gary Detlefs_, Jan 22 2013
%F A094567 a(n) = (2^(-n)*(5*(-2)^n+(7-3*sqrt(5))^n*(5-2*sqrt(5))+(5+2*sqrt(5))*(7+3*sqrt(5))^n))/15. - _Colin Barker_, Mar 05 2016
%e A094567 Obtain 4,30,203 from a(0)=1 and Fibonacci numbers 1,5,34,233: 4=5-1, 30=34-4, 203=233-30.
%t A094567 RecurrenceTable[{a[0]==1,a[n]==Fibonacci[4n+1]-a[n-1]},a[n],{n,30}] (* or *) LinearRecurrence[{6,6,-1},{1,4,30},31] (* _Harvey P. Dale_, Jul 13 2011 *)
%o A094567 (PARI) Vec(-(2*x-1)/((x+1)*(x^2-7*x+1)) + O(x^100)) \\ _Colin Barker_, Nov 19 2014
%o A094567 (PARI) vector(30, n, n--; (fibonacci(4*n+3) + (-1)^n)/3) \\ _Michel Marcus_, Nov 19 2014
%Y A094567 Cf. A000045, A094566.
%K A094567 nonn,easy
%O A094567 0,2
%A A094567 _Clark Kimberling_, May 12 2004
%E A094567 More terms from _Harvey P. Dale_, Jul 13 2011