A035302 a(n+1)=2a(n)-4a(n-1)+4a(n-2).

0, 1, -2, -8, -4, 16, 16, -48, -96, 64, 320, 0, -1024, -768, 2560, 4096, -5120, -16384, 4096, 53248, 24576, -147456, -180224, 327680, 786432, -458752, -2752512, -524288, 8126464, 7340032, -19922944, -36700160, 35651584

Offset

0,3

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2, -4, 4).

Formula

G.f.: (x-4*x^2)/(1-2*x+4*x^2-4*x^3).

Mathematica

LinearRecurrence[{2, -4, 4}, {0, 1, -2}, 40] (* Harvey P. Dale, Dec 01 2024 *)

Prog

(Haskell)
a035302 n = a035302_list !! (n-1)
a035302_list = 0 : 1 : (-2) :
   zipWith (+) (drop 2 $ map (* 2) a035302_list)
               (map (* 4) $ zipWith (-) a035302_list $ tail a035302_list)
-- Reinhard Zumkeller, Mar 18 2012
(PARI) a(n)=([0, 1, 0; 0, 0, 1; 4, -4, 2]^n*[0; 1; -2])[1, 1] \\ Charles R Greathouse IV, May 29 2026

Crossrefs

Cf. A007420.

Sequence in context: A209874 A175181 A110003 * A104772 A264142 A088156

Adjacent sequences: A035299 A035300 A035301 * A035303 A035304 A035305

Keyword

sign,easy

Author

N. J. A. Sloane

Status

approved