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A157614 a(n) = 29282*n^2 + 484*n + 1. 3
29767, 118097, 264991, 470449, 734471, 1057057, 1438207, 1877921, 2376199, 2933041, 3548447, 4222417, 4954951, 5746049, 6595711, 7503937, 8470727, 9496081, 10579999, 11722481, 12923527, 14183137, 15501311, 16878049, 18313351 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The identity (29282*n^2 + 484*n + 1)^2 - (121*n^2 + 2*n)*(2662*n + 22)^2 = 1 can be written as a(n)^2 - A181679(n)*A157613(n)^2 = 1 (see also Bruno Berselli's comment at A181679). - Vincenzo Librandi, Feb 21 2012
LINKS
Vincenzo Librandi, X^2-AY^2=1
FORMULA
From Vincenzo Librandi, Feb 21 2012: (Start)
G.f: x*(-29767 - 28796*x - x^2)/(x-1)^3;
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {29767, 118097, 264991}, 50] (* Vincenzo Librandi, Feb 21 2012 *)
PROG
(Magma) I:=[29767, 118097, 264991]; [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 21 2012
(PARI) for(n=1, 40, print1(29282*n^2+484*n+1", ")); \\ Vincenzo Librandi, Feb 21 2012
CROSSREFS
Sequence in context: A251054 A206070 A056747 * A209812 A258755 A251681
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 03 2009
STATUS
approved

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Last modified July 21 09:16 EDT 2024. Contains 374472 sequences. (Running on oeis4.)