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A117717
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Maximal number of regions obtained by a straight line drawing of the complete bipartite graph K_{n,n}.
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1
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0, 2, 13, 45, 116, 250, 477, 833, 1360, 2106, 3125, 4477, 6228, 8450, 11221, 14625, 18752, 23698, 29565, 36461, 44500, 53802, 64493, 76705, 90576, 106250, 123877, 143613
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This sequence is in the same spirit as A000127 where a formula is given for the maximal number of regions obtained by a straight line drawing of the complete graph K_n with the vertices located on the perimeter of a circle. This yields the often quoted sequence 1,2,4,8,16,31,...
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
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FORMULA
| a(n) = n^2 - 2n + C(n,2)^2 + 1
a(n) = (n-1)^2*(n^2+4)/4; [Vincenzo Librandi, Sep 09 2011]
G.f.: x^2*(2+3*x+x^3)/(1-x)^5. [Colin Barker, Feb 15 2012]
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MAPLE
| n^2-2*n+(numbcomb(n, 2))^2+1
a:=n->sum((n+j^3), j=1..n): seq(a(n), n=0..27); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 27 2006
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PROG
| (MAGMA)[(n-1)^2*(n^2+4)/4: n in [1..40]]; // Vincenzo Librandi, Sep 09 2011
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CROSSREFS
| Cf. A000127.
Sequence in context: A025194 A084156 A002534 * A176060 A168172 A005584
Adjacent sequences: A117714 A117715 A117716 * A117718 A117719 A117720
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KEYWORD
| nonn,changed
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AUTHOR
| Patricia A. Carey and Anant P. Godbole (petrepterodactyl(AT)gmail.com), Apr 13 2006
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