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

3,2

Links

Table of n, a(n) for n=3..35.

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.

Formula

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

Prog

(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

Crossrefs

Cf. A001623, A006519, A130077, A130079.

Sequence in context: A231777 A288181 A110622 * A230900 A204449 A172393

Adjacent sequences: A130075 A130076 A130077 * A130079 A130080 A130081

Keyword

nonn

Author

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

Status

approved