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199, 399, 599, 799, 999, 1199, 1399, 1599, 1799, 1999, 2199, 2399, 2599, 2799, 2999, 3199, 3399, 3599, 3799, 3999, 4199, 4399, 4599, 4799, 4999, 5199, 5399, 5599, 5799, 5999, 6199, 6399, 6599, 6799, 6999, 7199, 7399, 7599, 7799, 7999, 8199, 8399, 8599
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (200*n-1)^2-(100*n^2-n)*(20)^2=1 can be written as a(n)^2-A157659(n)*(20)^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
E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 14 in the first table at p. 85, case d(t) = t*(10^2*t-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*(199+x)/(1-x)^2.
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MATHEMATICA
| LinearRecurrence[{2, -1}, {199, 399}, 50]
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PROG
| (MAGMA) I:=[199, 399]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 200*n - 1.
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CROSSREFS
| Cf. A157659.
Sequence in context: A106759 A004926 A004946 * A033168 A140632 A142814
Adjacent sequences: A157952 A157953 A157954 * A157956 A157957 A157958
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 10 2009
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