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17, 71, 161, 287, 449, 647, 881, 1151, 1457, 1799, 2177, 2591, 3041, 3527, 4049, 4607, 5201, 5831, 6497, 7199, 7937, 8711, 9521, 10367, 11249, 12167, 13121, 14111, 15137, 16199, 17297, 18431, 19601, 20807, 22049, 23327, 24641, 25991, 27377, 28799
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (18*n^2-1)^2-(81*n^2-9)*(2*n)^2=1 can be written as a(n)^2-A157909(n)*A005843(n)^2=1. - Vincenzo Librandi, Feb 08 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
| G.f.: x*(-17-20*x+x^2)/(x - 1)^3. - Vincenzo Librandi, Feb 08 2012
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Feb 08 2012
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MATHEMATICA
| 18Range[40]^2-1 (* From Harvey P. Dale, Mar 24 2011 *)
LinearRecurrence[{3, -3, 1}, {17, 71, 161}, 50] (* Vincenzo Librandi, Feb 08 2012 *)
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PROG
| (MAGMA) I:=[17, 71, 161]; [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, Feb 08 2012
(PARI) for(n=1, 40, print1(18*n^2 - 1", ")); \\ Vincenzo Librandi, Feb 08 2012
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CROSSREFS
| Cf. A157909, A005843.
Sequence in context: A044010 A106921 A105414 * A141959 A069496 A047978
Adjacent sequences: A157907 A157908 A157909 * A157911 A157912 A157913
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 09 2009
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