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A157326
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10368n^2 + 288n + 1.
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3
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10657, 42049, 94177, 167041, 260641, 374977, 510049, 665857, 842401, 1039681, 1257697, 1496449, 1755937, 2036161, 2337121, 2658817, 3001249, 3364417, 3748321, 4152961, 4578337, 5024449, 5491297, 5978881, 6487201, 7016257
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OFFSET
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1,1
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COMMENTS
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The identity (10368*n^2+288*n+1)^2-(36*n^2+n)*(1728*n+24)^2=1 can be written as a(n)^2-A157324(n)*A157325(n)^2=1 (see also second part of the comment in A157324). - Vincenzo Librandi, Jan 26 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 to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Jan 26 2012
G.f.: x*(-x^2-10078*x-10657)/(x-1)^3. - Vincenzo Librandi, Jan 26 2012
a(n) = 2*A017533(6n)^2-1. - Bruno Berselli, Jan 29 2012
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {10657, 42049, 94177}, 50] (* Vincenzo Librandi, Jan 26 2012 *)
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PROG
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(MAGMA) I:=[10657, 42049, 94177]; [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 26 2012
(PARI) for(n=1, 22, print1(10368*n^2 + 288*n + 1", ")); \\ Vincenzo Librandi, Jan 26 2012
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CROSSREFS
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Cf. A157324, A157325.
Sequence in context: A013904 A138254 A154510 * A207261 A006006 A151411
Adjacent sequences: A157323 A157324 A157325 * A157327 A157328 A157329
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Feb 27 2009
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STATUS
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approved
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