OFFSET
0,2
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (11,-29).
FORMULA
a(n) = 11*a(n-1) - 29*a(n-2), a(0)=1, a(1)=6.
a(n) = (1/2 - sqrt(5)/10)*(11/2 - sqrt(5)/2)^n + (sqrt(5)/10 + 1/2)*(sqrt(5)/2 + 11/2)^n .
G.f.: (1-5*x)/(1-11*x+29*x^2).
a(n) = Sum_{k=0..n} A094441(n,k)*5^k. - Philippe Deléham, Dec 14 2009
MAPLE
seq(coeff(series((1-5*x)/(1-11*x+29*x^2), x, n+1), x, n), n = 0 .. 30); # G. C. Greubel, Aug 12 2019
MATHEMATICA
CoefficientList[Series[(1-5x)/(1 -11x +29x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 09 2013 *)
LinearRecurrence[{11, -29}, {1, 6}, 30] (* Harvey P. Dale, Aug 04 2022 *)
PROG
(Magma) I:=[1, 6]; [n le 2 select I[n] else 11*Self(n-1)-29*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Aug 09 2013
(PARI) my(x='x+O('x^30)); Vec((1-5*x)/(1-11*x+29*x^2)) \\ G. C. Greubel, Aug 12 2019
(Sage)
def A081570_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1-5*x)/(1-11*x+29*x^2)).list()
A081570_list(30) # G. C. Greubel, Aug 12 2019
(GAP) a:=[1, 6];; for n in [3..30] do a[n]:=11*a[n-1]-29*a[n-2]; od; a; # G. C. Greubel, Aug 12 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 22 2003
STATUS
approved