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A157816
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1482401250n^2 - 108900n + 1.
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3
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1482292351, 5929387201, 13341284551, 23717984401, 37059486751, 53365791601, 72636898951, 94872808801, 120073521151, 148239036001, 179369353351, 213464473201, 250524395551, 290549120401, 333538647751, 379492977601, 428412109951
(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 a(n)^2-A157814(n)* A157815(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*(-1482292351-1482510148*x-x^2)/(x-1)^3.
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {1482292351, 5929387201, 13341284551}, 30]
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PROG
| (MAGMA) I:=[1482292351, 5929387201, 13341284551]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..30]];
(PARI) a(n) = 1482401250*n^2 - 108900*n + 1.
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CROSSREFS
| Cf. A157814, A157815.
Sequence in context: A048051 A073519 A166113 * A157822 A034616 A084551
Adjacent sequences: A157813 A157814 A157815 * A157817 A157818 A157819
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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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