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A157436
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128n^2 + 2528n + 12481.
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3
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15137, 18049, 21217, 24641, 28321, 32257, 36449, 40897, 45601, 50561, 55777, 61249, 66977, 72961, 79201, 85697, 92449, 99457, 106721, 114241, 122017, 130049, 138337, 146881, 155681, 164737, 174049, 183617, 193441, 203521, 213857, 224449
(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 a(n)^2-A157434(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*(-12481*x^2-27362*x-15137)/(x-1)^3.
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {15137, 18049, 21217}, 50]
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PROG
| (MAGMA) I:=[15137, 18049, 21217]; [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) = 128*n^2 + 2528*n + 12481.
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CROSSREFS
| Cf. A157434, A157435.
Sequence in context: A004935 A004955 A004975 * A196495 A105924 A115924
Adjacent sequences: A157433 A157434 A157435 * A157437 A157438 A157439
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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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EXTENSIONS
| Corrected by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Jul 29 2010
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