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194, 780, 1758, 3128, 4890, 7044, 9590, 12528, 15858, 19580, 23694, 28200, 33098, 38388, 44070, 50144, 56610, 63468, 70718, 78360, 86394, 94820, 103638, 112848, 122450, 132444, 142830, 153608, 164778, 176340, 188294, 200640, 213378, 226508
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (196*n-1)^2-(196*n^2-2*n)*(14)^2=1 can be written as A158225(n)^2-a(n)*(14)^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 15 in the first table at p. 85, case d(t) = t*(14^2*t-2)).
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f.: x*(-194-198*x)/(x-1)^3.
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {194, 780, 1758}, 50]
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PROG
| (MAGMA) I:=[194, 780, 1758]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];
(PARI) a(n) = 196*n^2 - 2*n.
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CROSSREFS
| Cf. A158225.
Sequence in context: A023743 A025333 A025325 * A205621 A205356 A183583
Adjacent sequences: A158221 A158222 A158223 * A158225 A158226 A158227
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 14 2009
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