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A158589 a(n) = 324*n^2 - 18. 1
306, 1278, 2898, 5166, 8082, 11646, 15858, 20718, 26226, 32382, 39186, 46638, 54738, 63486, 72882, 82926, 93618, 104958, 116946, 129582, 142866, 156798, 171378, 186606, 202482, 219006, 236178, 253998, 272466, 291582, 311346, 331758, 352818, 374526, 396882, 419886 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The identity (36*n^2 - 1)^2 - (324*n^2 - 18)*(2*n)^2 = 1 can be written as A136017(n)^2 - a(n)* A005843(n)^2 = 1.
LINKS
Vincenzo Librandi, X^2-AY^2=1, Math Forum, 2007. [Wayback Machine link]
FORMULA
From Vincenzo Librandi, Feb 16 2012: (Start)
G.f.: -18*x*(17 + 20*x - x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
From Amiram Eldar, Mar 14 2023: (Start)
Sum_{n>=1} 1/a(n) = (1 - cot(Pi/(3*sqrt(2)))*Pi/(3*sqrt(2)))/36.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/(3*sqrt(2)))*Pi/(3*sqrt(2)) - 1)/36. (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {306, 1278, 2898}, 40] (* Vincenzo Librandi, Feb 16 2012 *)
324*Range[40]^2-18 (* Harvey P. Dale, Jul 25 2019 *)
PROG
(Magma) I:=[306, 1278, 2898]; [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 16 2012
(PARI) for(n=1, 40, print1(324*n^2 - 18", ")); \\ Vincenzo Librandi, Feb 16 2012
CROSSREFS
Sequence in context: A294710 A206271 A236012 * A030030 A206679 A172966
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 22 2009
EXTENSIONS
Comment rewritten by R. J. Mathar, Oct 28 2009
STATUS
approved

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Last modified June 15 22:50 EDT 2024. Contains 373412 sequences. (Running on oeis4.)