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A157854
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1728000n - 384240.
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3
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1343760, 3071760, 4799760, 6527760, 8255760, 9983760, 11711760, 13439760, 15167760, 16895760, 18623760, 20351760, 22079760, 23807760, 25535760, 27263760, 28991760, 30719760, 32447760, 34175760, 35903760, 37631760
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (103680000*n^2-46108800*n+5126401)^2-(3600*n^2-1601*n +178)*(1728000*n-384240)^2=1 can be written as A157855(n)^2-A157853(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*(1343760+384240*x)/(x-1)^2.
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MATHEMATICA
| LinearRecurrence[{2, -1}, {1343760, 3071760}, 40]
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PROG
| (MAGMA) I:=[1343760, 3071760]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 1728000*n - 384240.
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CROSSREFS
| Cf, A157853, A157855.
Sequence in context: A206620 A023047 A206254 * A184661 A187961 A120609
Adjacent sequences: A157851 A157852 A157853 * A157855 A157856 A157857
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 08 2009
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