OFFSET
1,2
COMMENTS
The corresponding values of y of this Pell equation are in A176374.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (97684,-1).
FORMULA
a(n) = 97684*a(n-1) - a(n-2) with a(1)=1, a(2)=48842.
From Bruno Berselli, Dec 14 2011: (Start)
G.f.: x*(1-48842*x)/(1-97684*x+x^2).
a(n) = ((221+27*r)^(2*n-2) + (221-27*r)^(2*n-2))/2^n, where r=sqrt(67). (End)
MAPLE
seq(coeff(series(x*(1-48842*x)/(1-97684*x+x^2), x, n+1), x, n), n = 1..15); # G. C. Greubel, Dec 08 2019
MATHEMATICA
LinearRecurrence[{97684, -1}, {1, 48842}, 15] (* G. C. Greubel, Dec 08 2019 *)
PROG
(Maxima) makelist(expand(((221+27*sqrt(67))^(2*n-2)+(221-27*sqrt(67))^(2*n-2))/2^n), n, 1, 9); /* Bruno Berselli, Dec 14 2011 */
(Magma) I:=[1, 48842]; [n le 2 select I[n] else 97684*Self(n-1)-Self(n-2): n in [1..15]]; // G. C. Greubel, Dec 08 2019
(PARI) my(x='x+O('x^15)); Vec(x*(1-48842*x)/(1-97684*x+x^2)) \\ G. C. Greubel, Dec 08 2019
(Sage)
def A176368_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x*(1-48842*x)/(1-97684*x+x^2) ).list()
a=A176368_list(15); a[1:] # G. C. Greubel, Dec 08 2019
(GAP) a:=[1, 48842];; for n in [3..15] do a[n]:=97684*a[n-1]-a[n-2]; od; a; # G. C. Greubel, Dec 08 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Apr 16 2010
STATUS
approved