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 A277692 Mendelsohn-Rodney sequence: number of court balanced tournament designs that are available for a given set of teams n. 1
 0, 1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 4, 1, 2, 3, 4, 1, 3, 1, 4, 3, 2, 1, 6, 2, 2, 3, 4, 1, 4, 1, 5, 3, 2, 3, 6, 1, 2, 3, 6, 1, 4, 1, 4, 5, 2, 1, 8, 2, 3, 3, 4, 1, 4, 3, 6, 3, 2, 1, 8, 1, 2, 5, 6, 3, 4, 1, 4, 3, 4, 1, 9, 1, 2, 5, 4, 3, 4, 1, 8, 4, 2, 1, 8, 3, 2, 3, 6, 1, 6, 3, 4, 3, 2, 3, 10, 1, 3, 5, 6, 1, 4, 1, 6, 7, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 E. Mendelsohn and P. Rodney, The existence of court balanced tournament designs, Discrete Mathematics, 133 (1994), 207-216. FORMULA a(n) is the number of values of c that satisfy the following conditions: C(n,2) mod c = 0, and (n-1) mod c = 0, and 1 <= c <= floor(n/2). a(2n) = A000005(2n-1)-1 for n > 1. - Chai Wah Wu, Oct 29 2016 EXAMPLE For n = 9, c = 1, 2, 4 satisfy the conditions given in the formula, so a(n) = 3. MATHEMATICA {0}~Join~Table[Function[k, Count[Range@ k, c_ /; And[Divisible[n - 1, c], Divisible[Binomial[n, 2], c]] ]]@ Floor[n/2], {n, 2, 108}] (* Michael De Vlieger, Oct 27 2016 *) PROG (Python 3.5) import scipy.stats teams = 151 courtcount = [] i= 1 for j in range(1, teams):     t = 0     for i in range(1, int(j/2) + 1):         if j>1 and ((j*(j-1))/2)%i == 0 and (j-1)%i == 0:             t += 1     if j > 1:         courtcount.append(t) a = 0 for p in courtcount:     if p == 1:         a+=1 print(courtcount) (PARI) a(n) = #select(x->(!(binomial(n, 2) % x)) && !((n-1) % x), vector(n\2, k, k)); \\ Michel Marcus, Oct 27 2016 (Python) from __future__ import division from sympy import divisors def A277692(n):     return sum(1 for c in divisors(n-1) if c < n-1 and not (n*(n-1)//2) % c) if n != 2 else 1 # Chai Wah Wu, Oct 29 2016 CROSSREFS Cf. A274332. Sequence in context: A252665 A001055 A320266 * A129138 A112970 A112971 Adjacent sequences:  A277689 A277690 A277691 * A277693 A277694 A277695 KEYWORD nonn AUTHOR Andrew G. McEachern, Oct 27 2016 STATUS approved

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Last modified March 25 20:10 EDT 2019. Contains 321477 sequences. (Running on oeis4.)