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%I #21 Jun 15 2016 11:25:06
%S 1,-3,-1,5,7,-3,-17,-11,23,45,-1,-91,-89,93,271,85,-457,-627,287,1541,
%T 967,-2115,-4049,181,8279,7917,-8641,-24475,-7193,41757,56143,-27371,
%U -139657,-84915,194399,364229,-24569,-753027,-703889,802165,2209943
%N Row sums of the Riordan array (1-4x+4x^2, x(1-2x)) (A167431).
%C The sequences A001607, A077020, A107920, A167433, A169998 are all essentially the same except for signs.
%C Variants are A107920 and A001607.
%H G. C. Greubel, <a href="/A167433/b167433.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,-2).
%F G.f.: (1-4x+4x^2)/(1-x+2x^2).
%F From _G. C. Greubel_, Jun 13 2016: (Start)
%F a(n) = a(n-1) - 2*a(n-2).
%F a(n) = -(2^((n+2)/2)/sqrt(7))*( 2*sin(n*arctan(sqrt(7))) + sqrt(2)*sin((n+1)*arctan(sqrt(7))) ), n>=1, and a(0)=1. (End)
%t a[n_] := Sin[n*ArcTan[Sqrt[7]]]; FullSimplify[Join[{1}, Table[- (2^(n/2 + 1)/Sqrt[7])*(2*a[n] + Sqrt[2]*a[n + 1]), {n, 1, 100}]]] (* or *) Join[{1}, LinearRecurrence[{1,-2},{-3,-1},100]] (* _G. C. Greubel_, Jun 13 2016 *)
%K easy,sign
%O 0,2
%A _Paul Barry_, Nov 03 2009
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