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A234943
Array read by antidiagonals: T(i,j) = size of optimal difference triangle set M(i,j).
12
1, 2, 3, 3, 7, 3, 4, 10, 13, 11, 5, 12, 19, 22, 17, 6, 15, 24, 32, 34, 25, 7, 19, 30, 41, 49, 51, 34, 8, 22, 36, 51, 64, 72, 70, 44, 9, 24, 42, 60, 79, 94, 100, 94, 55, 10, 27, 48, 71
OFFSET
1,2
COMMENTS
An (n,k) difference triangle set is a set of n blocks of k integers such that the difference sets of the blocks are all disjoint. The "scope" of such a set is defined to be the maximal element, if all blocks are translated such that their least elements are all 0. T(n,k) lists the minimal scope for which an (n,k) difference triangle set exists. - Charlie Neder, Jun 14 2019
REFERENCES
CRC Handbook of Combinatorial Designs, 1996, p. 315. (But beware errors!)
LINKS
Yeow Meng Chee and Charles J. Colbourn, Constructions for Difference Triangle Sets, arXiv:0712.2553 [cs.IT], 2007.
EXAMPLE
Array begins:
j\i| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
---+-----------------------------------------------------------------
1 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 (A000027)
2 | 3 7 10 12 15 19 22 24 27 31 34 36 39 43 46 (A013574)
3 | 6 13 19 24 30 36 42 48 54 60 66 72 78 84 90 (A013575)
4 | 11 22 32 41 51 60 71 80 91 100 111 120 131 140 151 (A013576)
5 | 17 34 49 64 79 (A013577)
6 | 25 51 72 94
7 | 34 70 100
8 | 44 94
9 | 55 121
10 | 72
11 | 85
12 | 106
13 | 127
14 | 151
15 | 177
CROSSREFS
For the number of different optimal triangle difference sets see the corresponding array in A234947.
Sequence in context: A140182 A340753 A239472 * A209494 A082910 A023646
KEYWORD
nonn,tabl,more
AUTHOR
N. J. A. Sloane, Jan 08 2014
STATUS
approved