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A157267
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10368n^2 - 4896n + 577.
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3
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6049, 32257, 79201, 146881, 235297, 344449, 474337, 624961, 796321, 988417, 1201249, 1434817, 1689121, 1964161, 2259937, 2576449, 2913697, 3271681, 3650401, 4049857, 4470049, 4910977, 5372641, 5855041, 6358177, 6882049
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (10368*n^2-4896*n+577)^2-(36*n^2-17*n+2)*(1728*n-408)^2=1 can be written as a(n)^2-A157265(n)*A157266(n)^2=1. - Vincenzo Librandi, Jan 27 2012
This is the case s=4n-1 of the identity (2*r^2-1)^2-((r^2-1)/144)*(24r)^2 = 1, where r=18*s+9*i^(s*(s+1))-(-1)^s-9 and i=sqrt(-1). - Bruno Berselli, Jan 29 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
| G.f.: x*(-6049-14110*x-577*x^2)/(x-1)^3. - Vincenzo Librandi, Jan 27 2012
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Jan 27 2012
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {6049, 32257, 79201}, 40] (* Vincenzo Librandi, Jan 27 2012 *)
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PROG
| (MAGMA) I:=[6049, 32257, 79201]; [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, Jan 27 2012
(PARI) for(n=1, 40, print1(10368*n^2 - 4896*n + 577", ")); \\ Vincenzo Librandi, Jan 27 2012
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CROSSREFS
| Cf. A157265, A157266.
Sequence in context: A157652 A175160 A184195 * A084804 A025515 A031666
Adjacent sequences: A157264 A157265 A157266 * A157268 A157269 A157270
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 26 2009
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