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A158729 a(n) = 1156*n^2 - 34. 2
1122, 4590, 10370, 18462, 28866, 41582, 56610, 73950, 93602, 115566, 139842, 166430, 195330, 226542, 260066, 295902, 334050, 374510, 417282, 462366, 509762, 559470, 611490, 665822, 722466, 781422, 842690, 906270, 972162, 1040366, 1110882, 1183710, 1258850, 1336302 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The identity (68*n^2 - 1)^2 - (1156*n^2 - 34)*(2*n)^2 = 1 can be written as A158730(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.: 34*x*(-33 - 36*x + x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
From Amiram Eldar, Mar 22 2023: (Start)
Sum_{n>=1} 1/a(n) = (1 - cot(Pi/sqrt(34))*Pi/sqrt(34))/68.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(34))*Pi/sqrt(34) - 1)/68. (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {1122, 4590, 10370}, 50] (* Vincenzo Librandi, Feb 20 2012 *)
PROG
(Magma) I:=[1122, 4590, 10370]; [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 20 2012
(PARI) for(n=1, 40, print1(1156*n^2 - 34", ")); \\ Vincenzo Librandi, Feb 20 2012
CROSSREFS
Sequence in context: A327431 A157444 A324404 * A346219 A035859 A105310
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 25 2009
EXTENSIONS
Comment rewritten and formula replaced by R. J. Mathar, Oct 22 2009
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)