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A157825
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1728000n - 1620240.
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3
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107760, 1835760, 3563760, 5291760, 7019760, 8747760, 10475760, 12203760, 13931760, 15659760, 17387760, 19115760, 20843760, 22571760, 24299760, 26027760, 27755760, 29483760, 31211760, 32939760, 34667760, 36395760
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (103680000*n^2-194428800*n+91152001)^2-(3600*n^2-6751*n+3165)*(1728000*n-1620240)^2=1 can be written as A157826(n)^2-A157824(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*(107760+1620240*x)/(x-1)^2.
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MATHEMATICA
| LinearRecurrence[{2, -1}, {107760, 1835760}, 40]
1728000Range[50]-1620240 (* From Harvey P. Dale, Mar 23 2011 *)
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PROG
| (MAGMA) I:=[107760, 1835760]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 1728000*n - 1620240.
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CROSSREFS
| Cf. A157824, A157826.
Sequence in context: A202404 A203882 A178284 * A205607 A205438 A102333
Adjacent sequences: A157822 A157823 A157824 * A157826 A157827 A157828
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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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