A133082 Triangle read by rows: T(k,m) = dimension of shape space for k labeled points in R^m (1 <= k <= m-1, m >= 2).

0, 1, 2, 2, 4, 5, 3, 6, 8, 9, 4, 8, 11, 13, 14, 5, 10, 14, 17, 19, 20, 6, 12, 17, 21, 24, 26, 27, 7, 14, 20, 25, 29, 32, 34, 35, 8, 16, 23, 29, 34, 38, 41, 43, 44, 9, 18, 26, 33, 39, 44, 48, 51, 53, 54, 10, 20, 29, 37, 44, 50, 55, 59, 62, 64, 65

Offset

2,3

References

D. G. Kendall et al., Shape and Shape Theory, Wiley, 1999; see p. 6.

Links

Table of n, a(n) for n=2..67.

Formula

The k-th column is an arithmetic progression with difference k.

Example

Triangle begins:
0
1 2
2 4 5
3 6 8 9
4 8 11 13 14
5 10 14 17 19 20
6 12 17 21 24 26 27
7 14 20 25 29 32 34 35
8 16 23 29 34 38 41 43 44
9 18 26 33 39 44 48 51 53 54
10 20 29 37 44 50 55 59 62 64 65

Crossrefs

Right-hand edge = A000096.

Sequence in context: A328728 A242348 A186053 * A347717 A130265 A368156

Adjacent sequences: A133079 A133080 A133081 * A133083 A133084 A133085

Keyword

nonn,tabl

Author

N. J. A. Sloane, Aug 24 2009

Status

approved