A087644 Triangle T(n,k) (n >= 2, 1 <= k <= n) read by rows: (1/2) times number of linearly inducible orderings of n points in k-dimensional Euclidean space.

1, 1, 3, 1, 6, 12, 1, 10, 36, 60, 1, 15, 86, 240, 360, 1, 21, 176, 756, 1800, 2520, 1, 28, 323, 1988, 7092, 15120, 20160, 1, 36, 547, 4572, 22996, 71856, 141120, 181440, 1, 45, 871, 9495, 64144, 278820, 787824, 1451520, 1814400, 1, 55, 1321, 18205, 159094

Offset: 2

Author

N. J. A. Sloane, Oct 26 2003

Keywords

• nonn
• tabl
• easy

Comments

Equals A071223/2. See that entry for further information.

Links

• T. M. Cover, The number of linearly inducible orderings of points in d-space, SIAM J. Applied Math., 15 (1967), 434-439.

Crossrefs

Cf. A071223.

Programs

Maple

T:=proc(n,k) if k>=n then 0 elif k=1 and n>=2 then 1 elif n=2 and k>=1 then 1 elif k=n-1 then n!/2 else T(n-1,k)+(n-1)*T(n-1,k-1) fi end:seq(seq(T(n,k),k=1..n-1),n=2..12);

Extensions

More terms from Emeric Deutsch, May 24 2004