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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.

%I A260333 #18 Aug 20 2015 08:23:15
%S A260333 1,1,1,7,6,2,1,19,87,115,30,6,1,37,417,1783,2902,1629,196,28,1,61,
%T A260333 1278,11758,50465,99717,84366,26836,2196,244,1,91,3060,49304,413473,
%U A260333 1841079,4277156,4929400,2572104,523432,27984,2544,1,127,6261,156633,2184561
%N 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.
%C A260333 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 A260333 Lars Blomberg, <a href="/A260333/b260333.txt">Table of n, a(n) for n = 0..89</a>
%H A260333 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 A260333 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 A260333 Triangle begins:
%e A260333 1,1,
%e A260333 1,7,6,2,
%e A260333 1,19,87,115,30,6,
%e A260333 1,37,417,1783,2902,1629,196,28,
%e A260333 1,61,1278,11758,50465,99717,84366,26836,2196,244,
%e A260333 1,91,3060,49304,413473,1841079,4277156,4929400,2572104,523432,27984,2544
%e A260333 ...
%Y A260333 A002047 is the right diagonal.
%Y A260333 The two nontrivial left diagonals are A003215 and A047786. The third is conjectured to be A260334.
%K A260333 nonn,tabf
%O A260333 0,4
%A A260333 _N. J. A. Sloane_, Jul 27 2015
%E A260333 More terms from _Lars Blomberg_, Aug 20 2015