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A167433
Row sums of the Riordan array (1-4x+4x^2, x(1-2x)) (A167431).
6
1, -3, -1, 5, 7, -3, -17, -11, 23, 45, -1, -91, -89, 93, 271, 85, -457, -627, 287, 1541, 967, -2115, -4049, 181, 8279, 7917, -8641, -24475, -7193, 41757, 56143, -27371, -139657, -84915, 194399, 364229, -24569, -753027, -703889, 802165, 2209943
OFFSET
0,2
COMMENTS
The sequences A001607, A077020, A107920, A167433, A169998 are all essentially the same except for signs.
Variants are A107920 and A001607.
FORMULA
G.f.: (1-4x+4x^2)/(1-x+2x^2).
From G. C. Greubel, Jun 13 2016: (Start)
a(n) = a(n-1) - 2*a(n-2).
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)
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A336301 A188146 A001607 * A077020 A107920 A169998
KEYWORD
easy,sign
AUTHOR
Paul Barry, Nov 03 2009
STATUS
approved