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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 7 21:19 EDT 2024. Contains 375017 sequences. (Running on oeis4.)