A000536 - OEIS

A000536

Number of 3-line Latin rectangles.
(Formerly M5152 N2236)

24, 240, 2520, 26880, 304080, 3671136, 47391120, 653463360, 9603708840, 150046937040, 2485510331304, 43536519673920, 804343214307360, 15636586027419840, 319143375070100640, 6824486562845878656, 152599994618389811640, 3561710724832153990320, 86627571138529803385080, 2192153071078356814538880, 57633178354598014299807984, 1572073330365520093029415200, 44434609885866805678475703600, 1299879247128621094998213278400, 39312834919322919649653205283400, 1227895179113516869799082638629776, 39569125440836907870479047149487560, 1314368274045259508166257769617810880, 44963797526832537006635800892057862720, 1582832153412276057834241761650127323520

(list; graph; refs; listen; history; text; internal format)

OFFSET

4,1

REFERENCES

Eggleton, Roger B. "Maximal Midpoint-Free Subsets of Integers." International Journal of Combinatorics Volume 2015, Article ID 216475, 14 pages; http://dx.doi.org/10.1155/2015/216475; http://www.hindawi.com/journals/ijcom/2015/216475/abs/

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).

LINKS

Table of n, a(n) for n=4..33.

Index entries for sequences related to Latin squares and rectangles

FORMULA

Let K(0,0)=1; K(n,0)=n*K(n-1,0)+(-1)^n, n>0; and j*K(n,j)=n*(n+1-2*j)*K(n-1,j-1)+n*(n-1)*K(n-2,j-1), j>0. Sequence is a(n)=K(n,2). - Sean A. Irvine, Nov 15 2010

MATHEMATICA

K[0, 0] = 1; K[n_, 0] := K[n, 0] = n*K[n-1, 0] + (-1)^n; K[n_, j_] := K[n, j] = (1/j)(n*(n+1-2*j)*K[n-1, j-1] + n*(n-1)*K[n-2, j-1]); a[n_] := K[n, 2]; Table[a[n], {n, 4, 33}] (* Jean-François Alcover, Feb 09 2016, after Sean A. Irvine *)

CROSSREFS

Sequence in context: A052520 A052724 A357242 * A151720 A052652 A052732

Adjacent sequences: A000533 A000534 A000535 * A000537 A000538 A000539

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Sean A. Irvine, Nov 15 2010

STATUS

approved