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A007533
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a(n) = (5n+1)^2 + 4n+1.
(Formerly M2162)
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2
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2, 41, 130, 269, 458, 697, 986, 1325, 1714, 2153, 2642, 3181, 3770, 4409, 5098, 5837, 6626, 7465, 8354, 9293, 10282, 11321, 12410, 13549, 14738, 15977, 17266, 18605, 19994, 21433, 22922, 24461, 26050, 27689, 29378
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OFFSET
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0,1
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COMMENTS
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Also, numbers of the form (3k+1)^2 + (4k+1)^2. - Bruno Berselli, Dec 11 2011
The continued fraction expansion of sqrt(a(n)) is [5n+1; {2, 2, 10n+2}]. For n=0, this collapses to [1; {2}]. - Magus K. Chu, Aug 27 2022
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REFERENCES
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W. Sierpiński, Elementary Theory of Numbers. Państ. Wydaw. Nauk., Warsaw, 1964, p. 323.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = 25n^2 + 14n + 2.
G.f.: (2 + 35*x + 13*x^2)/(1-x)^3. (End)
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MATHEMATICA
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Table[25n^2+14n+2, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {2, 41, 130}, 40] (* Harvey P. Dale, Dec 18 2013 *)
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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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