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A157796
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27225n^2 - 12098n + 1344.
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3
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16471, 86048, 210075, 388552, 621479, 908856, 1250683, 1646960, 2097687, 2602864, 3162491, 3776568, 4445095, 5168072, 5945499, 6777376, 7663703, 8604480, 9599707, 10649384, 11753511, 12912088, 14125115, 15392592, 16714519
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity(1482401250*n^2-658736100*n+73180801)^2-(27225*n^2-12098*n+1344)*(8984250*n-1996170)^2=1 can be written as A157798(n)^2-a(n)*A157797(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
| G.f.: x*(-16471-36635*x-1344*x^2)/(x-1)^3.
a(0)=16471, a(1)=86048, a(2)=210075, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) [From Harvey P. Dale, July 02 2011]
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MATHEMATICA
| Table[27225n^2-12098n+1344, {n, 25}] (* From Harvey P. Dale, Feb 20 2011 *)
LinearRecurrence[{3, -3, 1}, {16471, 86048, 210075}, 25] (* From Harvey P. Dale, July 02 2011 *)
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PROG
| (MAGMA) I:=[16471, 86048, 210075]; [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) = 27225*n^2 - 12098*n + 1344.
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CROSSREFS
| Cf. A157797, A157798.
Sequence in context: A168665 A031829 A057680 * A186848 A170779 A091089
Adjacent sequences: A157793 A157794 A157795 * A157797 A157798 A157799
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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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