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%I #17 Sep 08 2022 08:45:24
%S 0,2,13,45,116,250,477,833,1360,2106,3125,4477,6228,8450,11221,14625,
%T 18752,23698,29565,36461,44500,53802,64493,76705,90576,106250,123877,
%U 143613,165620,190066,217125,246977,279808,315810,355181,398125,444852,495578,550525
%N Maximal number of regions obtained by a straight line drawing of the complete bipartite graph K_{n,n}.
%C 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.
%H Vincenzo Librandi, <a href="/A117717/b117717.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = n^2 - 2n + C(n,2)^2 + 1
%F a(n) = (n-1)^2*(n^2+4)/4. - _Vincenzo Librandi_, Sep 09 2011
%F G.f.: x^2*(2+3*x+x^3)/(1-x)^5. - _Colin Barker_, Feb 15 2012
%F 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
%p A117717 := proc(n)
%p (n-1)^2*(n^2+4)/4 ;
%p end proc:
%p seq(A117717(n),n=1..10) ; # _R. J. Mathar_, Sep 15 2013
%t 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 *)
%o (Magma)[(n-1)^2*(n^2+4)/4: n in [1..40]]; // _Vincenzo Librandi_, Sep 09 2011
%Y Cf. A000127.
%K nonn,easy
%O 1,2
%A Patricia A. Carey and _Anant Godbole_, Apr 13 2006
%E More terms from _Harvey P. Dale_, Oct 16 2012
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