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A386875 a(n) is the maximum number of strong sub-tournaments in an n-tournament.

%I A386875 #16 Aug 26 2025 06:06:28
%S A386875 0,0,0,1,3,11,27,71,159,367,783,1695,3519,7359,15039,30847,62463,
%T A386875 126719,255231,514559,1033215,2075647,4160511,8341503,16703487,
%U A386875 33452031,66949119,133996543,268091391,536395775,1073004543,2146467839,4293394431,8587771903
%N A386875 a(n) is the maximum number of strong sub-tournaments in an n-tournament.
%D A386875 K. B. Reid and L. W. Beineke, "Tournaments", pp. 169-204 in L. W. Beineke and R. J. Wilson, editors, Selected Topics in Graph Theory, Academic Press, NY, 1978, p. 183 Corollary 6.2.
%H A386875 L. W. Beineke and F. Harary, <a href="https://doi.org/10.4153/CMB-1965-035-x">The Maximum Number of Strongly Connected Subtournaments</a>, Canadian Mathematical Bulletin, volume 8, Issue 4, 1965, pp. 491-498.
%H A386875 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,2,-12,4,12,-8).
%F A386875 a(n) = 2^n - n*2^((n - 1)/2) - 1 if n is odd, and a(n) = 2^n - 3*n*2^((n - 4)/2) - 1 if n is even.
%F A386875 G.f.: x^3/((2*x-1)*(x-1)*(2*x^2-1)^2). - _Alois P. Heinz_, Aug 06 2025
%F A386875 E.g.f.: cosh(2*x) - cosh(x) - x*cosh(sqrt(2)*x) - sinh(x) + sinh(2*x) - 3*x*sinh(sqrt(2)*x)/(2*sqrt(2)). - _Stefano Spezia_, Aug 11 2025
%F A386875 a(2n+1) = A286778(n)/2. - _R. J. Mathar_, Aug 26 2025
%t A386875 Table[If[Mod[n, 2] == 1, 2^n  - n*2^((n - 1)/2) - 1, 2^n - 3*n*2^((n - 4)/2) - 1], {n, 0, 20}]
%o A386875 (Maxima)
%o A386875 a(n) := if mod(n, 2) = 1 then 2^n - n*2^((n - 1)/2) - 1 else 2^n - 3*n*2^((n - 4)/2) - 1$
%o A386875 makelist(a(n), n, 1, 20);
%Y A386875 Cf. A006918 (the maximum number of 3-cycles in an (n+2)-tournament).
%Y A386875 Cf. A038376.
%K A386875 nonn,easy,changed
%O A386875 0,5
%A A386875 _Franck Maminirina Ramaharo_, Aug 06 2025