The On-Line Encyclopedia of Integer Sequences (OEIS)

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A130078

Largest 2^x dividing A001623(n), the number of reduced three-line Latin rectangles.
(history; published version)

#7 by Joerg Arndt at Mon Oct 02 08:25:54 EDT 2017

STATUS

proposed

approved

#6 by Michel Marcus at Mon Oct 02 08:21:36 EDT 2017

STATUS

editing

proposed

#5 by Michel Marcus at Mon Oct 02 08:21:29 EDT 2017

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.

#4 by Michel Marcus at Mon Oct 02 08:12:12 EDT 2017

REFERENCES

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.

LINKS

John Riordan, <a href="http://www.jstor.org/stable/2308187">A recurrence relation for three-line Latin rectangles</a>, Amer. Math. Monthly, 59 (1952), pp. 159-162.

D. S. Stones, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v17i1a1/0">The many formulas for the number of Latin rectangles</a>, Electron. J. Combin 17 (2010), A1.

D. S. Stones and I. M. Wanless, <a href="http://dx.doi.org/10.1016/j.jcta.2009.03.019">Divisors of the number of Latin rectangles</a>, J. Combin. Theory Ser. A 117 (2010), 204-215.

STATUS

approved

editing

#3 by N. J. A. Sloane at Thu Jun 16 23:27:32 EDT 2016

REFERENCES

D. S. Stones, The many formulae formulas for the number of Latin rectangles, Electron. J. Combin 17 (2010), A1.

Discussion

Thu Jun 16

23:27

OEIS Server: https://oeis.org/edit/global/2523

#2 by N. J. A. Sloane at Fri Aug 27 03:00:00 EDT 2010

REFERENCES

D. S. Stones, The many formulae 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.

KEYWORD

nonn,new

nonn

#1 by N. J. A. Sloane at Fri May 11 03:00:00 EDT 2007

NAME

Largest 2^x dividing A001623(n), the number of reduced three-line Latin rectangles.

DATA

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

REFERENCES

John Riordan, A recurrence relation for three-line Latin rectangles, Amer. Math. Monthly, 59 (1952), pp. 159-162.

CROSSREFS

Cf. A001623, A130077, A130079.

KEYWORD

nonn,new

AUTHOR

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

STATUS

approved