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, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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, k <= n/2} 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 A156525 A090732

Adjacent sequences: A000183 A000184 A000185 this_sequence A000187 A000188 A000189

nonn,nice,easy

N. J. A. Sloane (njas(AT)research.att.com).

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