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A157331
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128n^2 - 32n + 1.
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2
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97, 449, 1057, 1921, 3041, 4417, 6049, 7937, 10081, 12481, 15137, 18049, 21217, 24641, 28321, 32257, 36449, 40897, 45601, 50561, 55777, 61249, 66977, 72961, 79201, 85697, 92449, 99457, 106721, 114241, 122017, 130049, 138337, 146881
(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 a(n)^2-A033991(n)*A157330(n)^2=1 (see also the second part of the comment in A157330). - 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 (3,-3,1).
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FORMULA
| a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Jan 29 2012
G.f.: x*(-97-158*x-x^2)/(x-1)^3. - Vincenzo Librandi, Jan 29 2012
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {97, 449, 1057}, 40] (* Vincenzo Librandi, Jan 29 2012 *)
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PROG
| (MAGMA) I:=[97, 449, 1057]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jan 29 2012
(PARI) for(n=1, 40, print1(128*n^2 - 32*n + 1", ")); \\ Vincenzo Librandi, Jan 29 2012
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CROSSREFS
| Cf. A033991, A157330.
Sequence in context: A050666 A160440 A107213 * A142834 A125646 A142574
Adjacent sequences: A157328 A157329 A157330 * A157332 A157333 A157334
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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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