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 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, 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 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. 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); CROSSREFS Cf. A071223. Sequence in context: A106855 A064282 A267849 * A049964 A143984 A051124 Adjacent sequences:  A087641 A087642 A087643 * A087645 A087646 A087647 KEYWORD nonn,tabl,easy AUTHOR N. J. A. Sloane, Oct 26 2003 EXTENSIONS More terms from Emeric Deutsch, May 24 2004 STATUS approved

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