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A157665
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729n^2 - 1016n + 354.
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3
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67, 1238, 3867, 7954, 13499, 20502, 28963, 38882, 50259, 63094, 77387, 93138, 110347, 129014, 149139, 170722, 193763, 218262, 244219, 271634, 300507, 330838, 362627, 395874, 430579, 466742, 504363, 543442, 583979, 625974, 669427, 714338
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (531441*n^2-740664*n+258065)^2-(729*n^2-1016*n+354)*(19683*n-13716)^2=1 can be written as A157667(n)^2-a(n)*A157666(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*(-67-1037*x-354*x^2)/(x-1)^3.
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {67, 1238, 3867}, 40]
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PROG
| (MAGMA) I:=[67, 1238, 3867]; [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) = 729*n^2 - 1016*n + 354.
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CROSSREFS
| Cf. A157666, A157667.
Sequence in context: A166802 A093267 A032651 * A078850 A092795 A017783
Adjacent sequences: A157662 A157663 A157664 * A157666 A157667 A157668
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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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