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A157364
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4802n^2 - 196n + 1.
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3
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4607, 18817, 42631, 76049, 119071, 171697, 233927, 305761, 387199, 478241, 578887, 689137, 808991, 938449, 1077511, 1226177, 1384447, 1552321, 1729799, 1916881, 2113567, 2319857, 2535751, 2761249, 2996351, 3241057, 3495367
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (4802*n^2-196*n+1)^2-(49*n^2-2*n)*(686*n-14)^2=1 can be written as a(n)^2-A157362(n)*A157363(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*(-x^2-4996*x-4607)/(x-1)^3.
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {4607, 18817, 42631}, 50]
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PROG
| (MAGMA) I:=[4607, 18817, 42631]; [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) = 4802*n^2-196*n+1.
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CROSSREFS
| Cf. A157362, A157363.
Sequence in context: A204652 A032745 A020437 * A078094 A159205 A170795
Adjacent sequences: A157361 A157362 A157363 * A157365 A157366 A157367
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 28 2009
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