A135353 a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3), with a(0) = 2, a(1) = -3, a(2) = 3.

2, -3, 3, 22, 51, 93, 170, 333, 675, 1366, 2739, 5469, 10922, 21837, 43683, 87382, 174771, 349533, 699050, 1398093, 2796195, 5592406, 11184819, 22369629, 44739242, 89478477, 178956963, 357913942, 715827891, 1431655773, 2863311530, 5726623053, 11453246115, 22906492246

Offset

0,1

Comments

Sequence identical to its third differences. "Self-transform". Initial terms are transform's coefficients .

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) = (8/3)*2^n - (2/3)*cos(Pi*n/3) - (16*sqrt(3)/3)*sin(Pi*n/3). - Richard Choulet, Jan 02 2008

G.f.: (2 - 9*x + 18*x^2)/((1-2*x)*(1-x+x^2)). - Philippe Deléham, Dec 29 2008

Mathematica

LinearRecurrence[{3, -3, 2}, {2, -3, 3}, 30] (* or *) CoefficientList[Series[ (-2+9 x-18 x^2)/(-1+3 x-3 x^2+2 x^3), {x, 0, 30}], x] (* Harvey P. Dale, Apr 20 2011 *)

Crossrefs

Sequence in context: A062168 A296836 A019229 * A217705 A084956 A216724

Adjacent sequences: A135350 A135351 A135352 * A135354 A135355 A135356

Keyword

sign,changed

Author

Paul Curtz, Dec 07 2007

Extensions

More terms from Philippe Deléham, Dec 29 2008

Status

approved