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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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2
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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, 165620, 190066, 217125, 246977, 279808, 315810, 355181, 398125, 444852, 495578, 550525
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OFFSET
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1,2
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COMMENTS
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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 A000127.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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FORMULA
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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
a(n)=5*a(n-1)-10*a(n-2)+ 10*a(n-3)- 5*a(n-4)+a(n-5), n>5. - Harvey P. Dale, Oct 16 2012
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MAPLE
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A117717 := proc(n)
(n-1)^2*(n^2+4)/4 ;
end proc:
seq(A117717(n), n=1..10) ; # R. J. Mathar, Sep 15 2013
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MATHEMATICA
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Table[n^2-2n+Binomial[n, 2]^2+1, {n, 40}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {0, 2, 13, 45, 116}, 40] (* Harvey P. Dale, Oct 16 2012 *)
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PROG
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(Magma)[(n-1)^2*(n^2+4)/4: n in [1..40]]; // Vincenzo Librandi, Sep 09 2011
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CROSSREFS
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Cf. A000127.
Sequence in context: A084156 A002534 A212501 * A359252 A176060 A168172
Adjacent sequences: A117714 A117715 A117716 * A117718 A117719 A117720
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KEYWORD
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nonn,easy
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AUTHOR
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Patricia A. Carey and Anant Godbole, Apr 13 2006
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EXTENSIONS
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More terms from Harvey P. Dale, Oct 16 2012
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STATUS
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approved
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