

A130077


Largest x such that 2^x divides A001623(n), the number of reduced threeline Latin rectangles.


2



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
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OFFSET

3,2


LINKS

Table of n, a(n) for n=3..75.
John Riordan, A recurrence relation for threeline Latin rectangles, Amer. Math. Monthly, 59 (1952), pp. 159162.
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), 204215.


FORMULA

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


PROG

(PARI) a001623(n) = n*(n3)!*sum(i=0, n, sum(j=0, ni, (1)^j*binomial(3*i+j+2, j)<<(nij)/(nij)!)*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



