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27227, 108904, 245031, 435608, 680635, 980112, 1334039, 1742416, 2205243, 2722520, 3294247, 3920424, 4601051, 5336128, 6125655, 6969632, 7868059, 8820936, 9828263, 10890040, 12006267, 13176944, 14402071, 15681648, 17015675
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (1482401250*n^2+108900*n+1)^2-(27225*n^2+2*n)*(8984250*n+330)^2=1 can be written as A157822(n)^2-a(n)* A157821(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*(-27227-27223*x)/(x-1)^3.
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {27227, 108904, 245031}, 30]
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PROG
| (MAGMA) I:=[27227, 108904, 245031]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..30]];
(PARI) a(n) = 27225*n^2 + 2*n.
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CROSSREFS
| Cf. A157821, A157822.
Sequence in context: A186481 A127411 A157814 * A032746 A099230 A109481
Adjacent sequences: A157817 A157818 A157819 * A157821 A157822 A157823
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 07 2009
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EXTENSIONS
| Corrected by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Aug 09 2010
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