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56, 120, 184, 248, 312, 376, 440, 504, 568, 632, 696, 760, 824, 888, 952, 1016, 1080, 1144, 1208, 1272, 1336, 1400, 1464, 1528, 1592, 1656, 1720, 1784, 1848, 1912, 1976, 2040, 2104, 2168, 2232, 2296, 2360, 2424, 2488, 2552, 2616, 2680, 2744, 2808, 2872
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (128*n^2-32*n+1)^2-(4*n^2-n)*(64*n-8)^2=1 can be written as A157331(n)^2-A033991(n)*a(n)^2=1. This is the case s=2 of the identity (8*n^2*s^4-8*n*s^2+1)^2 -(n^2*s^2-n)*(8*n*s^3-4*s)^2 = 1. - Vincenzo Librandi, 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 (2,-1).
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FORMULA
| a(n) = 2*a(n-1)-a(n-2). - Vincenzo Librandi, Jan 29 2012
G.f.: x*(8*x+56)/(x-1)^2. - Vincenzo Librandi, Jan 29 2012
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MATHEMATICA
| LinearRecurrence[{2, -1}, {56, 120}, 50] (* Vincenzo Librandi, Jan 29 2012 *)
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PROG
| (MAGMA) I:=[56, 120]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jan 29 2012
(PARI) for(n=1, 40, print1(64*n - 8", ")); \\ Vincenzo Librandi, Jan 29 2012
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CROSSREFS
| Cf. A033991, A157331.
Sequence in context: A047779 A044243 A044624 * A038849 A003781 A030443
Adjacent sequences: A157327 A157328 A157329 * A157331 A157332 A157333
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 27 2009
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