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A001841 Related to Zarankiewicz's problem.
(Formerly M2460 N0977)

%I M2460 N0977

%S 3,5,10,14,21,26,36,43,55,64,78,88,105,117,136,150,171,186,210,227,

%T 253,272,300,320,351,373,406,430,465,490,528,555,595,624,666,696,741

%N Related to Zarankiewicz's problem.

%C Definition appears to be: a(n) is the maximum number of triangles in K_n, where each edge may be used 3 times. - _Charles R Greathouse IV_, Jul 06 2017

%D R. K. Guy, A problem of Zarankiewicz, in P. Erdős and G. Katona, editors, Theory of Graphs (Proceedings of the Colloquium, Tihany, Hungary), Academic Press, NY, 1968, pp. 119-150, (p. 126, divided by 2).

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H John Cerkan, <a href="/A001841/b001841.txt">Table of n, a(n) for n = 3..10000</a>

%H R. K. Guy, <a href="/A001197/a001197.pdf">A problem of Zarankiewicz</a>, Research Paper No. 12, Dept. of Math., Univ. Calgary, Jan. 1967. See p. 9 column t(3,m). [Annotated and scanned copy, with permission]

%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992.

%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992

%p A001841:=-(2*z**4+z**5+2*z**2+2*z**3+2*z+3)/(z**2-z+1)/(z**2+z+1)/(z+1)**2/(z-1)**3; # conjectured by _Simon Plouffe_ in his 1992 dissertation

%K nonn

%O 3,1

%A _N. J. A. Sloane_

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Last modified June 19 00:04 EDT 2021. Contains 345125 sequences. (Running on oeis4.)