A167433 Row sums of the Riordan array (1-4x+4x^2, x(1-2x)) (A167431).

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.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,-2).

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

Adjacent sequences: A167430 A167431 A167432 * A167434 A167435 A167436

Keyword

easy,sign

Author

Paul Barry, Nov 03 2009

Status

approved