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A158596 a(n) = 38*n^2 - 1. 2
37, 151, 341, 607, 949, 1367, 1861, 2431, 3077, 3799, 4597, 5471, 6421, 7447, 8549, 9727, 10981, 12311, 13717, 15199, 16757, 18391, 20101, 21887, 23749, 25687, 27701, 29791, 31957, 34199, 36517, 38911, 41381, 43927, 46549, 49247, 52021, 54871, 57797, 60799, 63877 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The identity (38*n^2 - 1)^2 - (361*n^2 - 19)*(2*n)^2 = 1 can be written as a(n)^2 - A158595(n)*A005843(n)^2 = 1.
LINKS
Vincenzo Librandi, X^2-AY^2=1, Math Forum, 2007. [Wayback Machine link]
FORMULA
G.f.: x*(-37 - 40*x + x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
From Amiram Eldar, Mar 14 2023: (Start)
Sum_{n>=1} 1/a(n) = (1 - cot(Pi/sqrt(38))*Pi/sqrt(38))/2.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(38))*Pi/sqrt(38) - 1)/2. (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {37, 151, 341}, 50] (* Vincenzo Librandi, Feb 16 2012 *)
PROG
(Magma) I:=[37, 151, 341]; [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(38*n^2 - 1", ")); \\ Vincenzo Librandi, Feb 16 2012
CROSSREFS
Sequence in context: A142656 A145898 A096700 * A142688 A178835 A250942
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 22 2009
EXTENSIONS
Comment rewritten, formula replaced by R. J. Mathar, Oct 28 2009
STATUS
approved

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Last modified May 20 01:37 EDT 2024. Contains 372703 sequences. (Running on oeis4.)