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A157626
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a(n) = 100n^2 - 151n + 57.
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3
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6, 155, 504, 1053, 1802, 2751, 3900, 5249, 6798, 8547, 10496, 12645, 14994, 17543, 20292, 23241, 26390, 29739, 33288, 37037, 40986, 45135, 49484, 54033, 58782, 63731, 68880, 74229, 79778, 85527, 91476, 97625, 103974, 110523, 117272, 124221
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OFFSET
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1,1
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COMMENTS
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The identity (80000*n^2-120800*n+45601)^2-(100*n.^2-151*n+57)*(8000*n-6040)^2=1 can be written as A157628(n)^2-a(n)*A157627(n)^2=1.
The continued fraction expansion of sqrt(a(n)) is [10n-8; {2, 4, 2, 20n-16}]. For n=1, this collapses to [2; {2, 4}]. - Magus K. Chu, Sep 05 2022
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LINKS
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FORMULA
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a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f.: x*(-6-137*x-57*x^2)/(x-1)^3.
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {6, 155, 504}, 40]
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PROG
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(Magma) I:=[6, 155, 504]; [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 - 151*n + 57.
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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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