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A168240
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a(n) = 13*n^2 + 7*n + 1.
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3
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21, 67, 139, 237, 361, 511, 687, 889, 1117, 1371, 1651, 1957, 2289, 2647, 3031, 3441, 3877, 4339, 4827, 5341, 5881, 6447, 7039, 7657, 8301, 8971, 9667, 10389, 11137, 11911, 12711, 13537, 14389, 15267, 16171, 17101, 18057, 19039, 20047, 21081, 22141, 23227
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OFFSET
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1,1
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COMMENTS
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Consider the quadratic cyclotomic polynomial f(x) = x^2+x+1 and the quotients defined by f(x + n*f(x))/f(x). a(n) is the quotient at x=3.
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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*(21+4*x+x^2)/(1-x)^3. (End)
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EXAMPLE
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f(x) = 13 when x = 3. Hence at n = 1, f(x + f(x))/f(x) = 21 = a(1).
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {21, 67, 139}, 50] (* G. C. Greubel, Apr 09 2016 *)
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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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EXTENSIONS
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Edited, definition simplified, sequence extended beyond a(8) by R. J. Mathar, Nov 23 2009
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STATUS
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approved
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