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.

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

3,1

Links

Table of n, a(n) for n=3..100.

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.

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

Crossrefs

Cf. A001623, A130077, A130078.

Sequence in context: A227471 A101403 A025509 * A350929 A365236 A247190

Adjacent sequences: A130076 A130077 A130078 * A130080 A130081 A130082

Keyword

nonn

Author

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

Status

approved