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A157440
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a(n) = 121*n^2 - 204*n + 86.
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3
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3, 162, 563, 1206, 2091, 3218, 4587, 6198, 8051, 10146, 12483, 15062, 17883, 20946, 24251, 27798, 31587, 35618, 39891, 44406, 49163, 54162, 59403, 64886, 70611, 76578, 82787, 89238, 95931, 102866, 110043, 117462, 125123, 133026, 141171
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OFFSET
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1,1
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COMMENTS
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The identity (14641*n^2 - 24684*n + 10405)^2 - (121*n^2 - 204*n + 86)*(1331*n - 1122)^2 = 1 can be written as A157442(n)^2 - a(n)*A157441(n)^2 = 1. - Vincenzo Librandi, Jan 29 2012
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Vincenzo Librandi, X^2-AY^2=1
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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G.f.: x*(-3 - 153*x - 86*x^2)/(x-1)^3. - Vincenzo Librandi, Jan 29 2012
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 29 2012
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {3, 162, 563}, 50] (* Vincenzo Librandi, Jan 29 2012 *)
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PROG
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(PARI) a(n)=121*n^2-204*n+86 \\ Charles R Greathouse IV, Dec 28 2011
(MAGMA) I:=[3, 162, 563]; [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
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CROSSREFS
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Cf. A157441, A157442.
Sequence in context: A303099 A302950 A173128 * A157559 A157586 A341224
Adjacent sequences: A157437 A157438 A157439 * A157441 A157442 A157443
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Mar 01 2009
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STATUS
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approved
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