A130078 -id:A130078 - cp's OEIS frontend

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

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

nonn

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.

Cf. A001623, A007814, A130078, A130079.

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

a(n) = A007814(A001623(n)). - Michel Marcus, Oct 02 2017

A130079 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.

Original entry on oeis.org

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, 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, 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

Offset: 3

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

nonn

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.

Cf. A001623, A130077, A130078.

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

cp's OEIS Frontend

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

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