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A156867
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a(n) = 729000*n - 180.
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4
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728820, 1457820, 2186820, 2915820, 3644820, 4373820, 5102820, 5831820, 6560820, 7289820, 8018820, 8747820, 9476820, 10205820, 10934820, 11663820, 12392820, 13121820, 13850820, 14579820, 15308820, 16037820, 16766820, 17495820
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OFFSET
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1,1
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COMMENTS
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The identity (32805000*n^2 - 16200*n + 1)^2 - (2025*n^2 - n)* (729000*n - 180)^2 = 1 can be written as A157080(n)^2 - A156855(n)*a(n)^2 = 1.
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LINKS
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FORMULA
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a(n) = 2*a(n-1) - a(n-2).
G.f.: x*(728820+180*x)/(1-x)^2.
E.g.f.: 180*(1 - (1 - 4050*x)*exp(x)). - G. C. Greubel, Jan 28 2022
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MATHEMATICA
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LinearRecurrence[{2, -1}, {728820, 1457820}, 40]
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PROG
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(Magma) I:=[728820, 1457820]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]];
(Sage) [180*(4050*n -1) for n in (1..40)] # G. C. Greubel, Jan 28 2022
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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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