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
Keywords
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).
Programs
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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 *)
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
Extensions
More terms from Philippe Deléham, Dec 29 2008
Comments