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 A109961 #8 Jun 13 2015 00:51:52
%S A109961 1,1,2,6,17,45,117,305,798,2090,5473,14329,37513,98209,257114,673134,
%T A109961 1762289,4613733,12078909,31622993,82790070,216747218,567451585,
%U A109961 1485607537,3889371025,10182505537,26658145586,69791931222,182717648081
%N A109961 Expansion of (1-x)^3/(1-4x+5x^2-4x^3+x^4).
%C A109961 Diagonal sums of number triangle A109960.
%H A109961 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,4,-1).
%F A109961 a(n)=sum{k=0..floor(n/2), binomial(n+2k, 4k)}.
%F A109961 a(0)=1, a(1)=1, a(2)=2, a(3)=6, a(n)=4*a(n-1)-5*a(n-2)+4*a(n-3)-a(n-4). - _Harvey P. Dale_, Dec 11 2013
%t A109961 CoefficientList[Series[(1-3x+3x^2-x^3)/(1-4x+5x^2-4x^3+x^4),{x,0,40}],x] (* or *) LinearRecurrence[{4,-5,4,-1},{1,1,2,6},40] (* _Harvey P. Dale_, Dec 11 2013 *)
%K A109961 easy,nonn
%O A109961 0,3
%A A109961 _Paul Barry_, Jul 06 2005