

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.


3



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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), 2331. [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: A152861 A285165 A198925 * 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



