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A156639
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a(n) = 169*n^2 - 140*n + 29.
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4
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58, 425, 1130, 2173, 3554, 5273, 7330, 9725, 12458, 15529, 18938, 22685, 26770, 31193, 35954, 41053, 46490, 52265, 58378, 64829, 71618, 78745, 86210, 94013, 102154, 110633, 119450, 128605, 138098, 147929, 158098
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OFFSET
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1,1
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COMMENTS
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The identity (57122*n^2 - 47320*n + 9801)^2 - (169*n^2 - 140*n + 29)*(4394*n - 1820)^2 = 1 can be written as A156721(n)^2 - a(n)*A156627(n)^2 = 1.
The continued fraction expansion of sqrt(a(n)) is [13n-6; {1, 1, 1, 1, 1, 1, 26n-12}]. - Magus K. Chu, Sep 06 2022
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LINKS
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FORMULA
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G.f.: x*(58 + 251*x + 29*x^2)/(1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {58, 425, 1130}, 40]
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PROG
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(Magma) I:=[58, 425, 1130]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..40]];
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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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EXTENSIONS
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STATUS
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approved
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