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A158597 a(n) = 400*n^2 - 20. 2
380, 1580, 3580, 6380, 9980, 14380, 19580, 25580, 32380, 39980, 48380, 57580, 67580, 78380, 89980, 102380, 115580, 129580, 144380, 159980, 176380, 193580, 211580, 230380, 249980, 270380, 291580, 313580, 336380, 359980, 384380, 409580, 435580, 462380, 489980, 518380 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The identity (40*n^2 - 1)^2 - (400*n^2 - 20)*(2*n)^2 = 1 can be written as A158598(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.: 20*x*(-19 - 22*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/(2*sqrt(5)))*Pi/(2*sqrt(5)))/40.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/(2*sqrt(5)))*Pi/(2*sqrt(5)) - 1)/40. (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {380, 1580, 3580}, 50] (* Vincenzo Librandi, Feb 16 2012 *)
400*Range[40]^2-20 (* Harvey P. Dale, Nov 04 2015 *)
PROG
(Magma) I:=[380, 1580, 3580]; [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(400*n^2- 20", ")); \\ Vincenzo Librandi, Feb 16 2012
CROSSREFS
Sequence in context: A206349 A252130 A252123 * A252122 A250635 A233952
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 19:00 EDT 2024. Contains 372720 sequences. (Running on oeis4.)