A260333 Irregular triangle read by rows: T(n,k) = number of ways k brooks (0 <= k <= 2n+1) can be placed on the grid points of an n triboard so that no two brooks lie in the same straight line.

1, 1, 1, 7, 6, 2, 1, 19, 87, 115, 30, 6, 1, 37, 417, 1783, 2902, 1629, 196, 28, 1, 61, 1278, 11758, 50465, 99717, 84366, 26836, 2196, 244, 1, 91, 3060, 49304, 413473, 1841079, 4277156, 4929400, 2572104, 523432, 27984, 2544, 1, 127, 6261, 156633, 2184561

Offset: 0

Author

N. J. A. Sloane, Jul 27 2015

Keywords

• nonn
• tabf

Comments

An "n triboard" is a hexagonal board or grid with n segments (and n+1 points) per side. - N. J. A. Sloane, Aug 20 2015

Examples

			Triangle begins:
1,1,
1,7,6,2,
1,19,87,115,30,6,
1,37,417,1783,2902,1629,196,28,
1,61,1278,11758,50465,99717,84366,26836,2196,244,
1,91,3060,49304,413473,1841079,4277156,4929400,2572104,523432,27984,2544
...
		

Links

• Lars Blomberg, Table of n, a(n) for n = 0..89
• B. T. Bennett and R. B. Potts, Arrays and brooks, J. Austral. Math. Soc., 7 (1967), 23-31. [Annotated scanned copy]

Crossrefs

A002047 is the right diagonal.

The two nontrivial left diagonals are A003215 and A047786. The third is conjectured to be A260334.

Formula

Bennett and Potts give formulas for the first two nontrivial diagonals on the left (A003215 and A047786), and conjectural formulas for the next two diagonals.

Extensions

More terms from Lars Blomberg, Aug 20 2015