A176901 Number of 3 X n semireduced Latin rectangles, that is, having exactly n fixed points in the first two rows.

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

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), 91-110.

V. S. Shevelev, Modern enumeration theory of permutations with restricted positions, Diskr. Mat., 1993, 5, no.1, 3-35 (Russian).

V. S. Shevelev, Modern enumeration theory of permutations with restricted positions, English translation, Discrete Math. and Appl., 1993, 3:3, 229-263 (pp. 255-257).

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_(n-k) * u_(n-2*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