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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Maximum number of regions determined by n bent lines (angular sectors). See GKP Reference.
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REFERENCES
| 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
| Guo-Niu Han, Enumeration of Standard Puzzles
Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n) = a(n-1)+4*n-3 (with a(0)=1) [From Vincenzo Librandi, Nov 23 2010]
a(n) = A000124(2*n)-2*n O.g.f.:(4*x^2-x+1)/(1-x)^3 [From Geoffrey Critzer, March 30 2011]
a(n) = 2*a(n-1)-a(n-2)+4. [From Eric Werley, Jun 27 2011]
a(0)=1, a(1)=2, a(2)=7, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) [From Harvey P. Dale, Jul 20 2011]
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MATHEMATICA
| a[n_]:=2*n^2-n+1; (* or *) Array[ -#*(1-#*2)+1&, 5!, 0] (* From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 21 2008 *)
LinearRecurrence[{3, -3, 1}, {1, 2, 7}, 50] (* From Harvey P. Dale, Jul 20 2011 *)
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CROSSREFS
| Cf. A084849.
Sequence in context: A048231 A070169 A162420 * A005581 A064468 A074470
Adjacent sequences: A130880 A130881 A130882 * A130884 A130885 A130886
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KEYWORD
| nonn,easy
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AUTHOR
| Mohammad K. Azarian (azarian(AT)evansville.edu), Jul 26 2007
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