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A176368
x-values in the solution to x^2 - 65*y^2 = 1.
3
1, 129, 33281, 8586369, 2215249921, 571525893249, 147451465208321, 38041906497853569, 9814664424981012481, 2532145379738603366529, 653283693308134687552001, 168544660728119010785049729
OFFSET
1,2
COMMENTS
The corresponding values of y of this Pell equation are in A176369.
FORMULA
a(n) = 258*a(n-1) - a(n-2) with a(1)=1, a(2)=129.
G.f.: x*(1-129*x)/(1-258*x+x^2).
MAPLE
seq(coeff(series(x*(1-129*x)/(1-258*x+x^2), x, n+1), x, n), n = 1..15); # G. C. Greubel, Dec 08 2019
MATHEMATICA
LinearRecurrence[{258, -1}, {1, 129}, 30]
PROG
(Magma) I:=[1, 129]; [n le 2 select I[n] else 258*Self(n-1)-Self(n-2): n in [1..20]];
(PARI) my(x='x+O('x^15)); Vec(x*(1-129*x)/(1-258*x+x^2)) \\ G. C. Greubel, Dec 08 2019
(Sage)
def A176368_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x*(1-129*x)/(1-258*x+x^2) ).list()
a=A176368_list(15); a[1:] # G. C. Greubel, Dec 08 2019
(GAP) a:=[1, 129];; for n in [3..15] do a[n]:=258*a[n-1]-a[n-2]; od; a; # G. C. Greubel, Dec 08 2019
CROSSREFS
Cf. A176369, Row 8 of array A188645.
Sequence in context: A264370 A196752 A143006 * A283535 A183553 A242229
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Apr 16 2010
STATUS
approved