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A157730
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441n^2 - 488n + 135.
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3
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88, 923, 2640, 5239, 8720, 13083, 18328, 24455, 31464, 39355, 48128, 57783, 68320, 79739, 92040, 105223, 119288, 134235, 150064, 166775, 184368, 202843, 222200, 242439, 263560, 285563, 308448, 332215, 356864, 382395, 408808, 436103, 464280
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity(388962*n^2-430416*n+119071)^2-(441*n^2-488*n+135)*(18522*n-10248)^2=1 can be written as A157732(n)^2-a(n)*A157731(n)^2=1.
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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).
G.f.: x*(-88-659*x-135*x^2)/(x-1)^3.
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {88, 923, 2640}, 40]
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PROG
| (MAGMA) I:=[88, 923, 2640]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n) = 441*n^2 - 488*n + 135.
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CROSSREFS
| Cf. 157731, A157732.
Sequence in context: A136933 A136958 A137049 * A055749 A182676 A107422
Adjacent sequences: A157727 A157728 A157729 * A157731 A157732 A157733
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 05 2009
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