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A156856
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a(n) = 2025*n^2 + n.
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5
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2026, 8102, 18228, 32404, 50630, 72906, 99232, 129608, 164034, 202510, 245036, 291612, 342238, 396914, 455640, 518416, 585242, 656118, 731044, 810020, 893046, 980122, 1071248, 1166424, 1265650, 1368926, 1476252, 1587628, 1703054, 1822530
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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 A157081(n)^2 - a(n)*A156868(n)^2 = 1.
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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.: 2*x*(1013 + 1012*x)/(1-x)^3. (End)
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {2026, 8102, 18228}, 40]
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PROG
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(Magma) I:=[2026, 8102, 18228]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(Sage) [n*(2025*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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