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 A117379 #5 Nov 08 2022 15:45:40
%S A117379 1,-4,1,-5,5,-6,10,-11,16,-21,27,-37,48,-64,85,-112,149,-197,261,-346,
%T A117379 458,-607,804,-1065,1411,-1869,2476,-3280,4345,-5756,7625,-10101,
%U A117379 13381,-17726,23482,-31107,41208
%N A117379 Expansion of (1-4x)/(1-x^2+x^3).
%C A117379 Diagonal sums of number triangle A117377.
%H A117379 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, -1).
%F A117379 a(n)=sum{k=0..floor(n/2), (-1)^n*(C(k,n-2k)+4*C(k, n-2k-1))}
%t A117379 CoefficientList[Series[(1-4x)/(1-x^2+x^3),{x,0,40}],x] (* or *) LinearRecurrence[ {0,1,-1},{1,-4,1},40] (* _Harvey P. Dale_, Nov 08 2022 *)
%K A117379 easy,sign
%O A117379 0,2
%A A117379 _Paul Barry_, Mar 10 2006