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167, 672, 1515, 2696, 4215, 6072, 8267, 10800, 13671, 16880, 20427, 24312, 28535, 33096, 37995, 43232, 48807, 54720, 60971, 67560, 74487, 81752, 89355, 97296, 105575, 114192, 123147, 132440, 142071, 152040, 162347, 172992, 183975, 195296
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (169*n-1)^2-(169*n^2-2*n)*(13)^2=1 can be written as A158219(n)^2-a(n)*(13)^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*(13^2*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*(-167-171*x)/(x-1)^3.
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {167, 672, 1515}, 50]
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PROG
| (MAGMA) I:=[167, 672, 1515]; [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) = 169*n^2 - 2*n.
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CROSSREFS
| Cf. A158219.
Sequence in context: A052233 A142431 A142776 * A142287 A167574 A201853
Adjacent sequences: A158215 A158216 A158217 * A158219 A158220 A158221
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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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