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51, 200, 447, 792, 1235, 1776, 2415, 3152, 3987, 4920, 5951, 7080, 8307, 9632, 11055, 12576, 14195, 15912, 17727, 19640, 21651, 23760, 25967, 28272, 30675, 33176, 35775, 38472, 41267, 44160, 47151, 50240, 53427, 56712, 60095, 63576, 67155
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (4802*n^2+196*n+1)^2-(49*n^2+2*n)*(686*n+14)^2=1 can be written as A157367(n)^2-a(n)*A157366(n)^2=1.
This formula is the case s=7 of the identity (2*s^4*n^2+4*s^2*n+1)^2-(s^2*n^2+2*n)*(2*s^3*n+2*s)^2=1. - Bruno Berselli, Feb 11 2012
Also, the identity (49*n+1)^2-(49*n^2+2*n)*7^2 = 1 can be written as A158066(n)^2-a(n)*7^2 = 1 (see Barbeau's paper in link). - Vincenzo Librandi, Feb 11 2012
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(7^2*t+2)).
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| G.f.: x*(51+47*x)/(1-x)^3.
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {51, 200, 447}, 50]
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PROG
| MAGMA) I:=[51, 200, 447]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n)=49*n^2+2*n \\ Charles R Greathouse IV, Dec 23 2011
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CROSSREFS
| Cf. A157366, A157367, A158066.
Sequence in context: A008883 A069762 A031431 * A157916 A007264 A158640
Adjacent sequences: A157362 A157363 A157364 * A157366 A157367 A157368
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 28 2009
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