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A157265
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a(n) = 36*n^2 - 17*n + 2.
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5
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21, 112, 275, 510, 817, 1196, 1647, 2170, 2765, 3432, 4171, 4982, 5865, 6820, 7847, 8946, 10117, 11360, 12675, 14062, 15521, 17052, 18655, 20330, 22077, 23896, 25787, 27750, 29785, 31892, 34071, 36322, 38645, 41040, 43507, 46046, 48657, 51340
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OFFSET
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1,1
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COMMENTS
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The identity (10368*n^2-4896*n+577)^2-(36*n^2-17*n+2)* (1728*n-408)^2=1 can be written as A157267(n)^2-a(n)* A157266(n)^2=1 (see also the second comment in A157267). - Vincenzo Librandi, Jan 27 2012
The continued fraction expansion of sqrt(a(n)) is [6n-2; {1, 1, 2, 1, 1, 12n-4}]. - Magus K. Chu, Sep 09 2022
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LINKS
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FORMULA
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E.g.f.: (36*x^2 + 19*x + 2)*exp(x) - 2. - G. C. Greubel, Feb 04 2018
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {21, 112, 275}, 40] (* Vincenzo Librandi, Jan 27 2012 *)
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PROG
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(Magma) I:=[21, 112, 275]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jan 27 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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