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A157509
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13122n^2 - 324n + 1.
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3
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12799, 51841, 117127, 208657, 326431, 470449, 640711, 837217, 1059967, 1308961, 1584199, 1885681, 2213407, 2567377, 2947591, 3354049, 3786751, 4245697, 4730887, 5242321, 5779999, 6343921, 6934087, 7550497, 8193151, 8862049
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (13122*n^2-324*n+1)^2-(81*n^2-2*n)*(1458*n-18)^2=1 can be written as a(n)^2-A157507(n)* A157508(n)^2=1. - Vincenzo Librandi, Jan 26 2012
This is the case s=9 of the identity (2*s^4*n^2-4*s^2*n+1)^2 - (s^2*n^2-2*n)*(2*s^3*n-2*s)^2 = 1. - Bruno Berselli, Jan 26 2011
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Vincenzo Librandi, X^2-AY^2=1
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Jan 26 2012
G.f.: x*(-12799-13444*x-x^2)/(x-1)^3. - Vincenzo Librandi, Jan 26 2012
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {12799, 51841, 117127}, 40] (* Vincenzo Librandi, Jan 26 2012 *)
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PROG
| (MAGMA) I:=[12799, 51841, 117127]; [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, Jan 26 2012
(PARI) for(n=1, 22, print1(13122n^2 - 324n + 1", ")); \\ Vincenzo Librandi, Jan 26 2012
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CROSSREFS
| Cf. A157507, A157508.
Sequence in context: A206796 A206966 A207133 * A035916 A204490 A024752
Adjacent sequences: A157506 A157507 A157508 * A157510 A157511 A157512
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 02 2009
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