A130077 Largest x such that 2^x divides A001623(n), the number of reduced three-line Latin rectangles.

0, 2, 1, 3, 4, 6, 5, 6, 7, 9, 8, 11, 13, 14, 12, 16, 15, 17, 16, 18, 19, 21, 20, 21, 22, 24, 23, 27, 27, 30, 27, 29, 31, 33, 32, 34, 35, 37, 36, 37, 38, 40, 39, 42, 44, 45, 43, 50, 46, 48, 47, 49, 50, 52, 51, 52, 53, 55, 54, 59, 58, 62, 58, 60, 63, 65, 64, 66, 67, 69, 68, 69, 70

Offset

3,2

Links

Table of n, a(n) for n=3..75.

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) = A007814(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) = valuation(a001623(n), 2); \\ Michel Marcus, Oct 02 2017

Crossrefs

Cf. A001623, A007814, A130078, A130079.

Sequence in context: A029636 A293517 A122514 * A080412 A300948 A098164

Adjacent sequences: A130074 A130075 A130076 * A130078 A130079 A130080

Keyword

nonn

Author

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

Status

approved