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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), 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: 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

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Last modified September 27 19:04 EDT 2020. Contains 337388 sequences. (Running on oeis4.)