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A157377
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531441n - 313146.
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3
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218295, 749736, 1281177, 1812618, 2344059, 2875500, 3406941, 3938382, 4469823, 5001264, 5532705, 6064146, 6595587, 7127028, 7658469, 8189910, 8721351, 9252792, 9784233, 10315674, 10847115, 11378556, 11909997, 12441438, 12972879
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (43046721*n^2-50729652*n+14945959)^2-(6561*n^2-7732*n+2278)*(531441*n-313146)^2=1 can be written as A157378(n)^2-A157376(n)*a(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 (2,-1).
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FORMULA
| a(n) = 2*a(n-1) -a(n-2).
G.f.: x*(218295+313146*x)/(x-1)^2.
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MATHEMATICA
| LinearRecurrence[{2, -1}, {218295, 749736}, 40]
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PROG
| (MAGMA) I:=[218295, 749736]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 531441*n - 313146.
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CROSSREFS
| Cf. A157376, A157378.
Sequence in context: A205734 A205915 A205907 * A090873 A072189 A187865
Adjacent sequences: A157374 A157375 A157376 * A157378 A157379 A157380
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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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