A130079 - OEIS

%I #9 Oct 02 2017 08:26:07

%S 3,2,4,3,3,2,4,4,4,3,5,3,2,2,5,2,4,3,5,4,4,3,5,5,5,4,6,3,4,2,6,5,4,3,

%T 5,4,4,3,5,5,5,4,6,4,3,3,6,0,5,4,6,5,5,4,6,6,6,5,7,3,5,2,7,6,4,3,5,4,

%U 4,3,5,5,5,4,6,4,1,3,6,4,5,4,6,5,5,4,6,6,6,5,7,4,5,3,7,6,5,4

%N a(n) = n - A130077(n), i.e., n minus the largest x such that 2^x divides A001623(n), the number of reduced three-line Latin rectangles.

%H John Riordan, <a href="http://www.jstor.org/stable/2308187">A recurrence relation for three-line Latin rectangles</a>, Amer. Math. Monthly, 59 (1952), pp. 159-162.

%H D. S. Stones, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v17i1a1/0">The many formulas for the number of Latin rectangles</a>, Electron. J. Combin 17 (2010), A1.

%H D. S. Stones and I. M. Wanless, <a href="http://dx.doi.org/10.1016/j.jcta.2009.03.019">Divisors of the number of Latin rectangles</a>, J. Combin. Theory Ser. A 117 (2010), 204-215.

%o (PARI) a001623(n) = n*(n-3)!*sum(i=0, n, sum(j=0, n-i, (-1)^j*binomial(3*i+j+2, j)<<(n-i-j)/(n-i-j)!)*i!);

%o a(n) = n - valuation(a001623(n), 2); \\ _Michel Marcus_, Oct 02 2017

%Y Cf. A001623, A130077, A130078.

%K nonn

%O 3,1

%A Douglas Stones (dssto1(AT)student.monash.edu.au), May 06 2007