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A157737
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a(n) = 441*n^2 - 2*n.
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4
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439, 1760, 3963, 7048, 11015, 15864, 21595, 28208, 35703, 44080, 53339, 63480, 74503, 86408, 99195, 112864, 127415, 142848, 159163, 176360, 194439, 213400, 233243, 253968, 275575, 298064, 321435, 345688, 370823, 396840, 423739, 451520
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OFFSET
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1,1
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COMMENTS
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The identity (441*n - 1)^2 - (441*n^2 - 2*n)*21^2 = 1 can be written as A158319(n)^2 - a(n)*21^2 = 1 (see Barbeau's paper in link). Also, the identity (388962*n^2 - 1764*n + 1)^2 - (441*n^2 - 2*n)*(18522*n - 42)^2 = 1 can be written as A157739(n)^2 - a(n)*A157738(n)^2 = 1. - Vincenzo Librandi, Jan 25 2012
This last formula is the case s=21 of the identity (2*s^4*n^2 - 4*s^2*n + 1)^2 - (s^2*n^2 - 2*n)*(2*s^3*n - 2*s)^2 = 1. - Bruno Berselli, Feb 05 2012
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LINKS
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FORMULA
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G.f.: x*(-439 - 443*x)/(x-1)^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}, {439, 1760, 3963}, 50]
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PROG
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(Magma) I:=[439, 1760, 3963]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];
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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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