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A157670
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531441n^2 - 322218n + 48842.
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3
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258065, 1530170, 3865157, 7263026, 11723777, 17247410, 23833925, 31483322, 40195601, 49970762, 60808805, 72709730, 85673537, 99700226, 114789797, 130942250, 148157585, 166435802, 185776901, 206180882, 227647745, 250177490
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (531441n^2-322218n+48842)^2-(729n^2-442n+67)*(19683n-5967)^2=1 can be written as a(n)^2-A157668(n)*A157669(n)^2=1.
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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).
G.f.: x*(-258065-755975*x-48842*x^2)/(x-1)^3.
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {258065, 1530170, 3865157}, 40]
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PROG
| (MAGMA) I:=[258065, 1530170, 3865157]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n) = 531441*n^2 - 322218*n + 48842.
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CROSSREFS
| Cf. A157668, A157669.
Sequence in context: A105657 A065794 A206253 * A153980 A184781 A146897
Adjacent sequences: A157667 A157668 A157669 * A157671 A157672 A157673
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 04 2009
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