A386875 a(n) is the maximum number of strong sub-tournaments in an n-tournament.
0, 0, 0, 1, 3, 11, 27, 71, 159, 367, 783, 1695, 3519, 7359, 15039, 30847, 62463, 126719, 255231, 514559, 1033215, 2075647, 4160511, 8341503, 16703487, 33452031, 66949119, 133996543, 268091391, 536395775, 1073004543, 2146467839, 4293394431, 8587771903
Offset: 0
References
- 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.
Links
- L. W. Beineke and F. Harary, The Maximum Number of Strongly Connected Subtournaments, Canadian Mathematical Bulletin, volume 8, Issue 4, 1965, pp. 491-498.
- Index entries for linear recurrences with constant coefficients, signature (3,2,-12,4,12,-8).
Programs
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Mathematica
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}] -
Maxima
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$ makelist(a(n), n, 1, 20);
Formula
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.
G.f.: x^3/((2*x-1)*(x-1)*(2*x^2-1)^2). - Alois P. Heinz, Aug 06 2025
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
a(2n+1) = A286778(n)/2. - R. J. Mathar, Aug 26 2025