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A157741
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a(n) = 388962*n^2 + 1764*n + 1.
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3
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390727, 1559377, 3505951, 6230449, 9732871, 14013217, 19071487, 24907681, 31521799, 38913841, 47083807, 56031697, 65757511, 76261249, 87542911, 99602497, 112440007, 126055441, 140448799, 155620081, 171569287, 188296417
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OFFSET
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1,1
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COMMENTS
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The identity (388962*n^2 + 1764*n + 1)^2 - (441*n^2 + 2*n)*(18522*n + 42)^2 = 1 can be written as a(n)^2 - A158321(n)*A157740(n)^2 = 1. - Vincenzo Librandi, Feb 05 2012
This is the case s=21 of the identity (2*n^2*s^4 + 4*n*s^2 + 1)^2 - (n^2*s^2 + 2*n)*(2*n*s^3 + 2*s)^2 = 1. - Vincenzo Librandi, Feb 05 2012
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LINKS
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FORMULA
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {390727, 1559377, 3505951}, 50] (* Vincenzo Librandi, Feb 05 2012 *)
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PROG
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(Magma) I:=[390727, 1559377, 3505951]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 05 2012
(PARI) for(n=1, 40, print1(388962*n^2 + 1764*n + 1", ")); \\ Vincenzo Librandi, Feb 05 2012
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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