A135446 a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3), with a(0) = a(1) = -1 and a(2) = 3.

-1, -1, 3, 10, 19, 33, 62, 125, 255, 514, 1027, 2049, 4094, 8189, 16383, 32770, 65539, 131073, 262142, 524285, 1048575, 2097154, 4194307, 8388609, 16777214, 33554429, 67108863, 134217730, 268435459, 536870913, 1073741822, 2147483645, 4294967295, 8589934594, 17179869187

Offset

0,3

Comments

Sequence identical to its third differences.

Links

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

Index entries for linear recurrences with constant coefficients, signature (3, -3, 2).

Formula

a(n+1) - 2*a(n) = hexaperiodic 1, 5, 4, -1, -5, -4, A130815.

a(n) = 2^n - 2*cos((Pi*n)/3) - (4*sqrt(3)/3)*sin((Pi*n)/3). Or, a(n) = 2^n + [ -2; -3; -1; 2; 3; 1]. - Richard Choulet, Dec 31 2007

G.f.: (1+x)*(1-3*x) / ( (2*x-1)*(x^2-x+1) ). - R. J. Mathar, Nov 07 2015

Mathematica

a = {-1, -1, 3}; Do[AppendTo[a, 3*a[[ -1]] - 3*a[[ -2]] + 2*a[[ -3]]], {40}]; a (* Stefan Steinerberger, Dec 22 2007 *)
LinearRecurrence[{3, -3, 2}, {-1, -1, 3}, 31] (* Ray Chandler, Sep 23 2015 *)

Crossrefs

Sequence in context: A028878 A010896 A234940 * A160002 A294421 A027177

Adjacent sequences: A135443 A135444 A135445 * A135447 A135448 A135449

Keyword

sign,easy

Author

Paul Curtz, Dec 13 2007

Status

approved