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A157843
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1728000n - 1343760.
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3
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384240, 2112240, 3840240, 5568240, 7296240, 9024240, 10752240, 12480240, 14208240, 15936240, 17664240, 19392240, 21120240, 22848240, 24576240, 26304240, 28032240, 29760240, 31488240, 33216240, 34944240, 36672240
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (103680000*n^2-161251200*n+62697601)^2-(3600*n^2-5599*n+2177)*(1728000*n-1343760)^2=1 can be written as A157844(n)^2-A157842(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*(384240+1343760*x)/(x-1)^2.
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MATHEMATICA
| LinearRecurrence[{2, -1}, {384240, 2112240}, 40]
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PROG
| (MAGMA) I:=[384240, 2112240]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 1728000*n - 1343760.
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CROSSREFS
| Cf. A157842, A157844.
Sequence in context: A206365 A205759 A205589 * A206167 A206381 A157739
Adjacent sequences: A157840 A157841 A157842 * A157844 A157845 A157846
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 07 2009
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