OFFSET
0,2
COMMENTS
Hankel transform of A168076.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-3,0,-27,-81).
FORMULA
a(n) = (-3)^n*A168074(n).
a(n) = 2*(-3)^n*n + 3^n*(sin(Pi*n/3)/sqrt(3) + cos(Pi*n/3)). - Ilya Gutkovskiy, Jul 10 2016
MATHEMATICA
LinearRecurrence[{-3, 0, -27, -81}, {1, -3, 36, -189}, 50] (* G. C. Greubel, Jul 09 2016 *)
CoefficientList[Series[(1 + 27 x^2 - 54 x^3) / ((1 + 3 x)^2 (1 - 3 x + 9 x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 10 2016 *)
PROG
(PARI) Vec((1+27*x^2-54*x^3)/((1+3*x)^2*(1-3*x+9*x^2))+ O(x^30)) \\ Michel Marcus, Dec 03 2014
(Magma) I:=[1, -3, 36, -189]; [n le 4 select I[n] else -3*Self(n-1)-27*Self(n-3)-81*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jul 10 2016
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Nov 18 2009
EXTENSIONS
Corrected by R. J. Mathar, Dec 03 2014
STATUS
approved