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A157434
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4n^2 + 79n + 390.
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3
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473, 564, 663, 770, 885, 1008, 1139, 1278, 1425, 1580, 1743, 1914, 2093, 2280, 2475, 2678, 2889, 3108, 3335, 3570, 3813, 4064, 4323, 4590, 4865, 5148, 5439, 5738, 6045, 6360, 6683, 7014, 7353, 7700, 8055, 8418, 8789, 9168, 9555, 9950, 10353, 10764
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (128*n^2+2528*n+12481)^2-(4*n^2+79*n+390)*(64*n+632)^2=1 can be written as A157436(n)^2-a(n)*A157435(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*(-390*x^2-855*x-473)/(x-1)^3
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {473, 564, 663}, 50]
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PROG
| (MAGMA) I:=[473, 564, 663]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];
(PARI) a(n) = 4*n^2 + 79*n + 390.
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CROSSREFS
| Cf. A157435, A157436.
Sequence in context: A180838 A006180 A074654 * A084629 A075286 A045302
Adjacent sequences: A157431 A157432 A157433 * A157435 A157436 A157437
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 01 2009
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