OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
P. S. Bruckman and G. C. Greubel, Advanced Problem H-725, Fibonacci Quarterly, 52(2):187-190, 2014.
Index entries for linear recurrences with constant coefficients, signature (4,0,0,-27).
FORMULA
a(n) = 3^n*(3*n + 5)/6 - (-1)^n*3^(n+1)/2*sin((n-1)*arcsin(sqrt(2/3)))/(6*sqrt(2)).
G.f.: 1/(1 - 4x + 27x^4).
a(n) = (1+3/n)*a(n-1) + (3+6/n)*a(n-2) + (9+9/n)*a(n-3). - Robert Israel, Oct 27 2014
MAPLE
gser := series(1/(1-4*x+27*x^4), x = 0, 35): seq(coeff(gser, x, n), n = 0 .. 30);
#Alternative:
F:= gfun[rectoproc]({(n+4)*a(n+4)+(-7-n)*a(n+3)+(-18-3*n)*a(n+2)+(-45-9*n)*a(n+1), a(0) = 1, a(1) = 4, a(2) = 16, a(3) = 64}, a(n), remember):
seq(F(n), n=0..100); # Robert Israel, Oct 27 2014
MATHEMATICA
CoefficientList[Series[1/(1 - 4 x + 27 x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 28 2014 *)
PROG
(PARI) Vec(1/(1-4*x+27*x^4)+O(x^99)) \\ Charles R Greathouse IV, Oct 28 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Oct 27 2014
STATUS
approved