A130078 Largest 2^x dividing A001623(n), the number of reduced three-line Latin rectangles.

1, 4, 2, 8, 16, 64, 32, 64, 128, 512, 256, 2048, 8192, 16384, 4096, 65536, 32768, 131072, 65536, 262144, 524288, 2097152, 1048576, 2097152, 4194304, 16777216, 8388608, 134217728, 134217728, 1073741824, 134217728, 536870912, 2147483648

Offset: 3

Author

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

Keywords

• nonn

Links

• John Riordan, A recurrence relation for three-line Latin rectangles, Amer. Math. Monthly, 59 (1952), pp. 159-162.
• D. S. Stones, The many formulas for the number of Latin rectangles, Electron. J. Combin 17 (2010), A1.
• D. S. Stones and I. M. Wanless, Divisors of the number of Latin rectangles, J. Combin. Theory Ser. A 117 (2010), 204-215.

Crossrefs

Cf. A001623, A006519, A130077, A130079.

Programs

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!);
a(n) = 2^valuation(a001623(n), 2); \\ Michel Marcus, Oct 02 2017

Formula

a(n) = A006519(A001623(n)). - Michel Marcus, Oct 02 2017