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A158773 a(n) = 1600*n^2 - 40. 2
1560, 6360, 14360, 25560, 39960, 57560, 78360, 102360, 129560, 159960, 193560, 230360, 270360, 313560, 359960, 409560, 462360, 518360, 577560, 639960, 705560, 774360, 846360, 921560, 999960, 1081560, 1166360, 1254360, 1345560, 1439960, 1537560, 1638360, 1742360 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The identity (80*n^2 - 1)^2 - (1600*n^2 - 40)*(2*n)^2 = 1 can be written as A158774(n)^2 - a(n)*A005843(n)^2 = 1.
LINKS
Vincenzo Librandi, X^2-AY^2=1, Math Forum, 2007. [Wayback Machine link]
FORMULA
G.f.: 40*x*(-39 - 42*x + x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
From Amiram Eldar, Mar 24 2023: (Start)
Sum_{n>=1} 1/a(n) = (1 - cot(Pi/(2*sqrt(10)))*Pi/(2*sqrt(10)))/80.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/(2*sqrt(10)))*Pi/(2*sqrt(10)) - 1)/80. (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {1560, 6360, 14360}, 50] (* Vincenzo Librandi, Feb 21 2012 *)
1600*Range[30]^2-40 (* Harvey P. Dale, Apr 30 2017 *)
PROG
(Magma) I:=[1560, 6360, 14360]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 21 2012
(PARI) for(n=1, 40, print1(1600*n^2 - 40", ")); \\ Vincenzo Librandi, Feb 21 2012
CROSSREFS
Sequence in context: A302057 A092001 A069475 * A259303 A035865 A031800
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 26 2009
EXTENSIONS
Comment rewritten and formula replaced by R. J. Mathar, Oct 22 2009
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)