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A158669 a(n) = 900*n^2 - 30. 2
870, 3570, 8070, 14370, 22470, 32370, 44070, 57570, 72870, 89970, 108870, 129570, 152070, 176370, 202470, 230370, 260070, 291570, 324870, 359970, 396870, 435570, 476070, 518370, 562470, 608370, 656070, 705570, 756870, 809970, 864870, 921570, 980070, 1040370, 1102470 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The identity (60*n^2 - 1)^2 - (900*n^2 - 30)*(2*n)^2 = 1 can be written as A158670(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.: 30*x*(-29 - 32*x + x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
From Amiram Eldar, Mar 20 2023: (Start)
Sum_{n>=1} 1/a(n) = (1 - cot(Pi/sqrt(30))*Pi/sqrt(30))/60.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(30))*Pi/sqrt(30) - 1)/60. (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {870, 3570, 8070}, 50] (* Vincenzo Librandi, Feb 18 2012 *)
PROG
(Magma) I:=[870, 3570, 8070]; [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 18 2012
(PARI) for(n=1, 40, print1(900*n^2 - 30", ")); \\ Vincenzo Librandi, Feb 18 2012
CROSSREFS
Sequence in context: A165377 A283449 A351878 * A206172 A205426 A035855
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 24 2009
EXTENSIONS
Comment rephrased and redundant formula replaced by R. J. Mathar, Oct 19 2009
STATUS
approved

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Last modified March 28 17:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)