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Search: a130078 -id:a130078
Displaying 1-2 of 2 results found.
page 1
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A130077
Largest x such that 2^x divides A001623(n), the number of reduced three-line Latin rectangles.
+10
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
(list; graph; refs; listen; history; text; internal format)
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.
KEYWORD
nonn
AUTHOR
Douglas Stones (dssto1(AT)student.monash.edu.au), May 06 2007
STATUS
approved
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.
+10
2
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
(list; graph; refs; listen; history; text; internal format)
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.
KEYWORD
nonn
AUTHOR
Douglas Stones (dssto1(AT)student.monash.edu.au), May 06 2007
STATUS
approved
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