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A157443
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121n^2 - 38n + 3.
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3
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86, 411, 978, 1787, 2838, 4131, 5666, 7443, 9462, 11723, 14226, 16971, 19958, 23187, 26658, 30371, 34326, 38523, 42962, 47643, 52566, 57731, 63138, 68787, 74678, 80811, 87186, 93803, 100662, 107763, 115106, 122691, 130518, 138587, 146898
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (14641*n^2-4598*n+362)^2-(121*n^2-38*n+3)*(1331*n-209)^2=1 can be written as A157445(n)^2-a(n)*A157444(n)^2=1. - Vincenzo Librandi, Jan 26 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 26 2012
G.f.: x*(-86-153*x-3*x^2)/(x-1)^3. - Vincenzo Librandi, Jan 26 2012
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {86, 411, 978}, 40] (* Vincenzo Librandi, Jan 26 2012 *)
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PROG
| (MAGMA) I:=[86, 411, 978]; [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 26 2012
(PARI) for(n=1, 22, print1(121*n^2 - 38*n + 3", ")); \\ Vincenzo Librandi, Jan 26 2012
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CROSSREFS
| Cf. A157444, A157445.
Sequence in context: A113690 A043379 A162028 * A035136 A202524 A202769
Adjacent sequences: A157440 A157441 A157442 * A157444 A157445 A157446
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 01 2009
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