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90, 390, 890, 1590, 2490, 3590, 4890, 6390, 8090, 9990, 12090, 14390, 16890, 19590, 22490, 25590, 28890, 32390, 36090, 39990, 44090, 48390, 52890, 57590, 62490, 67590, 72890, 78390, 84090, 89990, 96090, 102390, 108890, 115590, 122490, 129590
(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 A158491(n)^2-a(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: 10*x*(-9-12*x+x^2)/(x-1)^3.
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EXAMPLE
| For n=1, a(1)=90; n=2, a(2)=390; n=3, a(3)=890
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {90, 390, 890}, 20]
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PROG
| (MAGMA) I:=[90, 390, 890]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
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CROSSREFS
| Cf. A005843, A158491.
Sequence in context: A157888 A201103 A179962 * A187300 A203741 A203734
Adjacent sequences: A158487 A158488 A158489 * A158491 A158492 A158493
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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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