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

0,4

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

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]

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.

Example

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
...

Crossrefs

A002047 is the right diagonal.

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

Sequence in context: A285165 A198925 A355923 * A138096 A258010 A011102

Adjacent sequences: A260330 A260331 A260332 * A260334 A260335 A260336

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jul 27 2015

Extensions

More terms from Lars Blomberg, Aug 20 2015

Status

approved