

A117717


Maximal number of regions obtained by a straight line drawing of the complete bipartite graph K_{n,n}.


3



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

1,2


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 A000127.


LINKS



FORMULA

a(n) = n^2  2n + C(n,2)^2 + 1
a(n)=5*a(n1)10*a(n2)+ 10*a(n3) 5*a(n4)+a(n5), n>5.  Harvey P. Dale, Oct 16 2012


MAPLE

(n1)^2*(n^2+4)/4 ;
end proc:


MATHEMATICA

Table[n^22n+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 *)


PROG



CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



