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19, 79, 179, 319, 499, 719, 979, 1279, 1619, 1999, 2419, 2879, 3379, 3919, 4499, 5119, 5779, 6479, 7219, 7999, 8819, 9679, 10579, 11519, 12499, 13519, 14579, 15679, 16819, 17999, 19219, 20479, 21779, 23119, 24499, 25919, 27379, 28879, 30419
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (20*n^2-1)^2-(100*n^2-10)*(2*n)^2=1 can be written as a(n)^2-A158490(n)*A005843(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*(-19-22*x+x^2)/(x-1)^3
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {19, 79, 179}, 50]
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PROG
| (MAGMA) I:=[19, 79, 179]; [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)=20*n^2-1 \\ Charles R Greathouse IV, Dec 23 2011
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CROSSREFS
| Cf. A005843, A158490.
Sequence in context: A074822 A139871 A142789 * A201783 A139941 A127270
Adjacent sequences: A158488 A158489 A158490 * A158492 A158493 A158494
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 20 2009
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