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