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A154377
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a(n) = 25*n^2 + 2*n.
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4
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27, 104, 231, 408, 635, 912, 1239, 1616, 2043, 2520, 3047, 3624, 4251, 4928, 5655, 6432, 7259, 8136, 9063, 10040, 11067, 12144, 13271, 14448, 15675, 16952, 18279, 19656, 21083, 22560, 24087, 25664, 27291, 28968, 30695, 32472, 34299, 36176
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OFFSET
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1,1
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COMMENTS
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The identity (1250*n^2 + 100*n + 1)^2 - (25*n^2 + 2*n)*(250*n + 10)^2 = 1 can be written as A154375(n)^2 - a(n)*A154379(n)^2 = 1 (see also the second comment in A154375). - Vincenzo Librandi, Jan 30 2012
The continued fraction expansion of sqrt(4*a(n)) is [10n; {2, 1, 1, 5n-1, 1, 1, 2, 20n}]. - Magus K. Chu, Sep 27 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*(27 + 23*x)/(1-x)^3.
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {27, 104, 231}, 50]
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PROG
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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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