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A157511
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5000n^2 + 200n + 1.
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3
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5201, 20401, 45601, 80801, 126001, 181201, 246401, 321601, 406801, 502001, 607201, 722401, 847601, 982801, 1128001, 1283201, 1448401, 1623601, 1808801, 2004001, 2209201, 2424401, 2649601, 2884801, 3130001, 3385201, 3650401
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (5000n^2+200n+1)^2-(25n^2+n)*(1000n+20)^2=1 can be written as a(n)^2-A173089(n)*A157510(n)^2=1 (see also second part of the comment in A173089). - Vincenzo Librandi, Feb 04 2012
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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 (3,-3,1).
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FORMULA
| Contribution by Harvey P. Dale, May 24 2011: (Start)
a(1)=5201, a(2)=20401, a(3)=45601, a(n)=3*a(n-1)-3*a(n-2)+a(n-3).
G.f.: -x*((5201+x*(4798+x))/(x-1)^3). (End)
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MATHEMATICA
| Table[5000n^2+200n+1, {n, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {5201, 20401, 45601}, 40] (* From Harvey P. Dale, May 24 2011 *)
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PROG
| (MAGMA) I:=[5201, 20401, 45601]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 04 2012
(PARI) for(n=1, 40, print1(5000*n^2 + 200*n + 1", ")); \\ Vincenzo Librandi, Feb 04 2012
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CROSSREFS
| Cf. A157510, A173089.
Sequence in context: A066167 A028549 A093071 * A165599 A109159 A067224
Adjacent sequences: A157508 A157509 A157510 * A157512 A157513 A157514
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 02 2009
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