0,4

K. P. Bogart and J. Q. Longyear, Counting 3 by n Latin rectangles, Proc. Amer. Math. Soc., 54 (1976), 463-467.

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 183.

Goulden and Jackson, Combin. Enum., Wiley, 1983 p. 284.

S. M. Jacob, The enumeration of the Latin rectangle of depth three..., Proc. London Math. Soc., 31 (1928), 329-336.

S. M. Kerawala, The enumeration of the Latin rectangle of depth three by means of a difference equation, Bull. Calcutta Math. Soc., 33 (1941), 119-127.

S. M. Kerawala, The asymptotic number of three-deep Latin rectangles, Bull. Calcutta Math. Soc., 39 (1947), 71-72.

Koichi, Yamamoto, An asymptotic series for the number of three-line Latin rectangles, J. Math. Soc. Japan 1, (1950). 226-241.

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 210.

N. J. A. Sloane, Table of n, a(n) for n = 0..207

Index entries for sequences related to Latin squares and rectangles

a(n)=n!*Sum_{k+j<=n} (2^j/j!)*k!*binomial(-3*(k+1), n-k-j).

a(n) = Sum_{k=0..n} D(n-k)*D(k)*U(n-2*k), where D() = A000166, U() = A000179 (Riordan, p. 209).

for n from 1 to 250 do t0:=0; for j from 0 to n do for k from 0 to n-j do t0:=t0 + (2^j/j!)*k!*binomial(-3*(k+1), n-k-j); od: od: t0:=n!*t0; lprint(n, t0); od:

Cf. A000512.

Sequence in context: A138450 A054946 A046744 this_sequence A012113 A090732 A014298

Adjacent sequences: A000183 A000184 A000185 this_sequence A000187 A000188 A000189

nonn,nice,easy

njas

Formula and more terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 31 2001