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A130883
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a(n) = 2*n^2 - n + 1.
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29
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1, 2, 7, 16, 29, 46, 67, 92, 121, 154, 191, 232, 277, 326, 379, 436, 497, 562, 631, 704, 781, 862, 947, 1036, 1129, 1226, 1327, 1432, 1541, 1654, 1771, 1892, 2017, 2146, 2279, 2416, 2557, 2702, 2851, 3004, 3161, 3322, 3487, 3656, 3829
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OFFSET
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0,2
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COMMENTS
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Maximum number of regions determined by n bent lines (angular sectors). See GKP Reference.
a(n)*Pi is the total length of half circle spiral after n rotations. It is formed as irregular spiral with two center points. At the 2nd stage, there are two alternatives: (1) select 2nd half circle radius, r2 = 2, the sequence will be A014105 or (2) select r2 = 0, the sequence will be A130883. See illustration in links. - Kival Ngaokrajang, Jan 19 2014
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REFERENCES
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R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, 2nd ed., Addison-Wesley, Reading, MA, 1994, pp7-8.
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LINKS
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FORMULA
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a(n) = 2*a(n-1) - a(n-2) + 4. - Eric Werley, Jun 27 2011
a(0)=1, a(1)=2, a(2)=7; for n > 2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Jul 20 2011
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {1, 2, 7}, 50] (* Harvey P. Dale, Jul 20 2011 *)
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PROG
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(Haskell)
(Python)
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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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