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A195025
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a(n) = n*(14*n + 3).
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7
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0, 17, 62, 135, 236, 365, 522, 707, 920, 1161, 1430, 1727, 2052, 2405, 2786, 3195, 3632, 4097, 4590, 5111, 5660, 6237, 6842, 7475, 8136, 8825, 9542, 10287, 11060, 11861, 12690, 13547, 14432, 15345, 16286, 17255, 18252, 19277, 20330, 21411, 22520
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OFFSET
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0,2
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COMMENTS
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Sequence found by reading the line from 0, in the direction 0, 17, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. This is the one of the semi-axis of the square spiral, which is related to the primitive Pythagorean triple [3, 4, 5].
a(k) is a square for k=(3/56)*((449+120*sqrt(14))^n+(449-120*sqrt(14))^n-2). - Bruno Berselli, Oct 18 2011
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LINKS
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FORMULA
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a(n) = 14*n^2 + 3*n.
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MATHEMATICA
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Table[n(14n+3), {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 17, 62}, 50] (* Harvey P. Dale, Jul 17 2023 *)
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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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STATUS
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approved
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