OFFSET
0,3
COMMENTS
Binomial transform of A083085.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-2,8).
FORMULA
a(n) = (2*2^n + (-4)^n)/3.
G.f.: (1+2*x)/((1+4*x)*(1-2*x)).
E.g.f.: (2*exp(2*x) + exp(-4*x))/3.
a(n) = -2*a(n-1) + 8*a(n-2). - Vincenzo Librandi, Nov 12 2011
MATHEMATICA
LinearRecurrence[{-2, 8}, {1, 0}, 41] (* G. C. Greubel, Feb 19 2023 *)
PROG
(Magma) [(2*2^n+(-4)^n)/3: n in [0..30]]; // Vincenzo Librandi, Nov 12 2011
(PARI) a(n)=(2*2^n+(-4)^n)/3 \\ Charles R Greathouse IV, Oct 07 2015
(SageMath) [(2^(n+1)+(-4)^n)/3 for n in range(41)] # G. C. Greubel, Feb 19 2023
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Paul Barry, Apr 23 2003
STATUS
approved