%I #33 Jan 04 2025 13:48:02
%S 0,2,3,5,7,9,10,12,13,15,17,18,19,21,22,25,26,27,29,30,32,34,35,37,38,
%T 40,42,43,44,46,47,50,51,52,54,55,57,59,60,62,63,65,67,68,69,71,72,75,
%U 76,77,79,80,82,84,85,87,88,90,92,93,94,96,97,100,101,102
%N Maximum frustration of complete bipartite graph K(n,5).
%C The maximum frustration of a graph is the maximum cardinality of a set of edges that contains at most half the edges of any cut-set. Another term that is used is "line index of imbalance". It is also equal to the covering radius of the coset code of the graph.
%H Robert Israel, <a href="/A245227/b245227.txt">Table of n, a(n) for n = 1..10000</a>
%H G. S. Bowlin, <a href="https://doi.org/10.37236/2204">Maximum Frustration in Bipartite Signed Graphs</a>, Electr. J. Comb. 19(4) (2012) #P10.
%H R. L. Graham and N. J. A. Sloane, <a href="http://www.math.ucsd.edu/~ronspubs/85_01_covering_radius.pdf">On the Covering Radius of Codes</a>, IEEE Trans. Inform. Theory, IT-31(1985), 263-290.
%H P. Solé and T. Zaslavsky, <a href="https://doi.org/10.1137/S0895480189174374">A Coding Approach to Signed Graphs</a>, SIAM J. Discr. Math 7 (1994), 544-553.
%F a(n) = floor(25/16*n) - 1 if n == 2,4,9,13, or 15 mod 16 or if n = 1 or 3; a(n) = floor(25/16*n) otherwise.
%F G.f.: -x^2*(x^18-x^17+x^16-x^15-3*x^14-x^13-2*x^12-x^11-x^10-2*x^9-2*x^8-x^7-2*x^6-x^5-2*x^4-2*x^3-2*x^2-x-2)/(x^17-x^16-x+1).
%F a(n+16) = a(n) + 25 for n > 3.
%F a(n) = A245230(max(n,5),min(n,5)).
%e For n=2 a set of edges that attains the maximum cardinality a(2)=2 is {(1,3),(1,4)}.
%p A245227:= n -> floor(25/16*n) - piecewise(member(n mod 16, {2,4,9,13,15}),1,0):
%p A245227(1):= 0:
%p A245227(3):= 3:
%p seq(A245227(n),n=1..100);
%t a[n_] := Floor[25 n/16] - If[n == 1 || n == 3 || MemberQ[{2, 4, 9, 13, 15}, Mod[n, 16]], 1, 0];
%t Array[a, 100] (* _Jean-François Alcover_, Mar 27 2019, after _Robert Israel_ *)
%Y Cf. A245230, A245231, A245239, A245314.
%K nonn
%O 1,2
%A _Robert Israel_, Jul 14 2014