%I #12 Oct 11 2019 15:15:01

%S 1,-2,-4,1,7,1,-12,-7,18,20,-23,-45,21,88,1,-154,-68,241,223,-327,

%T -532,345,1082,-140,-1959,-597,3181,2416,-4543,-6194,5308,13153,-3657,

%U -24655,-4188,41465,25186,-61932,-70839,78211,157957,-69304,-307007,-10442,534268

%N Expansion of (1 - 3x)/(1 - x + 2x^2 - x^3).

%C Row sums of number triangle A119302.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,-2,1).

%F a(n) = a(n-1) - 2a(n-2) + a(n-3);

%F a(n) = Sum_{k=0..n} (C(2k, n-k) + 3*C(2k, n-k-1))*(-1)^(n-k).

%t RecurrenceTable[{a[0]==1, a[1]== -2, a[2]== -4, a[n]== a[n-1] - 2*a[n-2] + a[n-3]}, a, {n,30}] (* _G. C. Greubel_, Aug 07 2015 *)

%t LinearRecurrence[{1,-2,1},{1,-2,-4},50] (* _Harvey P. Dale_, Oct 11 2019 *)

%K easy,sign

%O 0,2

%A _Paul Barry_, May 13 2006