

A176901


Number of 3 X n semireduced Latin rectangles, that is, having exactly n fixed points in the first two rows.


0



4, 72, 1584, 70720, 3948480, 284570496, 25574768128, 2808243910656, 369925183388160, 57585548812887040, 10458478438093154304, 2191805683821733404672, 525011528578874444283904, 142540766765931981615759360, 43542026550306796238178877440, 14867182204795857282384287236096, 5640920219495105293649671985430528
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OFFSET

3,1


COMMENTS

A Latin rectangle is called reduced if its first row is [1,2,...,n] (the number of 3 X n reduced Latin rectangles is given in A000186). Therefore a Latin rectangle having exactly n fixed points in the first two rows may be called "semireduced". Thus if A1(i), A2(i), i=1,...,n, are the first two rows, then, for every i, either A1(i)=i or A2(i)=i.


LINKS

Table of n, a(n) for n=3..19.
V. S. Shevelev, Reduced Latin rectangles and square matrices with equal row and column sums, Diskr. Mat.(J. of the Akademy of Sciences of Russia) 4(1992), 91110.
V. S. Shevelev, Modern enumeration theory of permutations with restricted positions, Diskr. Mat., 1993, 5, no.1, 335 (Russian).
V. S. Shevelev, Modern enumeration theory of permutations with restricted positions, English translation, Discrete Math. and Appl., 1993, 3:3, 229263 (pp. 255257).


FORMULA

Let F_n = A087981(n) = n! * Sum_{2*k_2+...+n*k_n=n, k_i>=0} Product_{i=2..n} 2^k_i/(k_i!*i^k_i). Then a(n) = Sum_{k=0..floor(n/2)} binomial(n,k) * F_k * F_(nk) * u_(n2*k), where u(n) = A000179(n).  Vladimir Shevelev, Mar 30 2016


CROSSREFS

Cf. A174563, A000179, A000186, A087981, A094047, A174556, A174560, A174561.
Sequence in context: A307358 A201976 A328426 * A304316 A186415 A211038
Adjacent sequences: A176898 A176899 A176900 * A176902 A176903 A176904


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Apr 28 2010


EXTENSIONS

More terms from William P. Orrick, Jul 25 2020


STATUS

approved



