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A157651
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100n^2 - 49n + 6.
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3
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57, 308, 759, 1410, 2261, 3312, 4563, 6014, 7665, 9516, 11567, 13818, 16269, 18920, 21771, 24822, 28073, 31524, 35175, 39026, 43077, 47328, 51779, 56430, 61281, 66332, 71583, 77034, 82685, 88536, 94587, 100838, 107289, 113940, 120791, 127842
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (80000*n^2-39200*n+4801)^2-(100*n^2-49*n+6)*(8000*n-1960)^2=1 can be written as A157653(n)^2-a(n)*A157652(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*(-57-137*x-6*x^2)/(x-1)^3.
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {57, 308, 759}, 40]
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PROG
| (MAGMA) I:=[57, 308, 759]; [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) = 100*n^2 - 49*n + 6.
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CROSSREFS
| Cf. A157652, A157653.
Sequence in context: A145296 A176635 A048422 * A043399 A038482 A097200
Adjacent sequences: A157648 A157649 A157650 * A157652 A157653 A157654
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 03 2009
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