

A117717


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


2



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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

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).


FORMULA

a(n) = n^2  2n + C(n,2)^2 + 1
a(n) = (n1)^2*(n^2+4)/4.  Vincenzo Librandi, Sep 09 2011
G.f.: x^2*(2+3*x+x^3)/(1x)^5.  Colin Barker, Feb 15 2012
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

A117717 := proc(n)
(n1)^2*(n^2+4)/4 ;
end proc:
seq(A117717(n), n=1..10) ; # R. J. Mathar, Sep 15 2013


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

(Magma)[(n1)^2*(n^2+4)/4: n in [1..40]]; // Vincenzo Librandi, Sep 09 2011


CROSSREFS

Cf. A000127.
Sequence in context: A084156 A002534 A212501 * A359252 A176060 A168172
Adjacent sequences: A117714 A117715 A117716 * A117718 A117719 A117720


KEYWORD

nonn,easy


AUTHOR

Patricia A. Carey and Anant Godbole, Apr 13 2006


EXTENSIONS

More terms from Harvey P. Dale, Oct 16 2012


STATUS

approved



