A260333 - OEIS

%I #18 Aug 20 2015 08:23:15

%S 1,1,1,7,6,2,1,19,87,115,30,6,1,37,417,1783,2902,1629,196,28,1,61,

%T 1278,11758,50465,99717,84366,26836,2196,244,1,91,3060,49304,413473,

%U 1841079,4277156,4929400,2572104,523432,27984,2544,1,127,6261,156633,2184561

%N 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.

%C 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

%H Lars Blomberg, <a href="/A260333/b260333.txt">Table of n, a(n) for n = 0..89</a>

%H B. T. Bennett and R. B. Potts, <a href="/A002047/a002047_1.pdf">Arrays and brooks</a>, J. Austral. Math. Soc., 7 (1967), 23-31. [Annotated scanned copy]

%F 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.

%e Triangle begins:

%e 1,1,

%e 1,7,6,2,

%e 1,19,87,115,30,6,

%e 1,37,417,1783,2902,1629,196,28,

%e 1,61,1278,11758,50465,99717,84366,26836,2196,244,

%e 1,91,3060,49304,413473,1841079,4277156,4929400,2572104,523432,27984,2544

%e ...

%Y A002047 is the right diagonal.

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

%K nonn,tabf

%O 0,4

%A _N. J. A. Sloane_, Jul 27 2015

%E More terms from _Lars Blomberg_, Aug 20 2015