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 A105370 #12 Dec 10 2024 05:32:52
%S A105370 1,-1,1,-2,5,-10,15,-15,0,50,-175,450,-1000,2000,-3625,5875,-8125,
%T A105370 8125,0,-29375,106250,-278125,621875,-1243750,2250000,-3640625,
%U A105370 5031250,-5031250,0,18203125,-65859375,172421875,-385546875,771093750,-1394921875,2257031250,-3119140625,3119140625,0
%N A105370 Expansion of ((1+x)^4-(1+x)x^3)/((1+x)^5-x^5).
%C A105370 Binomial transform is A105367. Consecutive pair sums of 105369.
%H A105370 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-5,-10,-10,-5).
%F A105370 G.f.: (1+x)(1+3x+3x^2)/(1+5x+10x^2+10x^3+5x^4).
%F A105370 a(n) = (5/2-sqrt(5)/2)^(n/2)((1/2+sqrt(5)/10)cos(7*Pi*n/10)+ sqrt(1/10-sqrt(5)/50)sin(7*Pi*n/10))- (5/2+sqrt(5)/2)^(n/2)((sqrt(5)/10-1/2)cos(9*Pi*n/10)+sqrt(1/10+sqrt(5)/50)sin(9*Pi*n/10)).
%F A105370 a(0)=1, a(1)=-1, a(2)=1, a(3)=-2, a(n)=-5*a(n-1)-10*a(n-2)- 10*a(n-3)- 5*a(n-4). - _Harvey P. Dale_, May 23 2012
%t A105370 CoefficientList[Series[((1+x)^4-(1+x)x^3)/((1+x)^5-x^5),{x,0,40}],x] (* or *) LinearRecurrence[{-5,-10,-10,-5},{1,-1,1,-2},41] (* _Harvey P. Dale_, May 23 2012 *)
%K A105370 easy,sign
%O A105370 0,4
%A A105370 _Paul Barry_, Apr 01 2005