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A158639
a(n) = 676*n^2 - 26.
2
650, 2678, 6058, 10790, 16874, 24310, 33098, 43238, 54730, 67574, 81770, 97318, 114218, 132470, 152074, 173030, 195338, 218998, 244010, 270374, 298090, 327158, 357578, 389350, 422474, 456950, 492778, 529958, 568490, 608374, 649610, 692198, 736138, 781430, 828074
OFFSET
1,1
COMMENTS
The identity (52*n^2 - 1)^2 - (676*n^2 - 26)*(2*n)^2 = 1 can be written as A158640(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.: 26*x*(-25 - 28*x + x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
From Amiram Eldar, Mar 19 2023: (Start)
Sum_{n>=1} 1/a(n) = (1 - cot(Pi/sqrt(26))*Pi/sqrt(26))/52.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(26))*Pi/sqrt(26) - 1)/52. (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {650, 2678, 6058}, 50] (* Vincenzo Librandi, Feb 17 2012 *)
PROG
(Magma) I:=[650, 2678, 6058]; [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 17 2012
(PARI) for(n=1, 40, print1(676*n^2 - 26", ")); \\ Vincenzo Librandi, Feb 17 2012
CROSSREFS
Sequence in context: A114047 A288142 A157915 * A162025 A251861 A035851
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 23 2009
EXTENSIONS
Comment rephrased and redundant formula replaced by R. J. Mathar, Oct 19 2009
STATUS
approved