cp's OEIS Frontend

A234350 Triangle T(n, k) = Number of non-equivalent (mod D_3) ways to arrange k indistinguishable points on a triangular grid of side n so that no three points are collinear. Triangle read by rows.

%I A234350 #20 Feb 01 2014 04:46:50
%S A234350 1,1,1,1,2,4,5,2,3,10,22,24,8,1,4,22,77,153,140,47,2,5,41,217,713,
%T A234350 1290,1112,322,15,7,72,530,2557,7374,11743,8783,2412,143,1,8,116,1149,
%U A234350 7661,32477,82988,116154,77690,19621,1220,5,10,180,2288,20055,116420,433372
%N A234350 Triangle T(n, k) = Number of non-equivalent (mod D_3) ways to arrange k indistinguishable points on a triangular grid of side n so that no three points are collinear. Triangle read by rows.
%C A234350 The triangle T(n, k) is irregularly shaped: 1 <= k <= A234349(n). First row corresponds to n = 1.
%C A234350 The maximal number of points that can be placed on a triangular grid of side n so that no three points are collinear is given by A234349(n).
%C A234350 Without the restriction "non-equivalent (mod D_3)" the numbers are given by A194136.
%H A234350 Heinrich Ludwig, <a href="/A234350/b234350.txt">Table of n, a(n) for n = 1..152</a>
%e A234350 Triangle begins
%e A234350 1;
%e A234350 1,   1,    1;
%e A234350 2,   4,    5,    2;
%e A234350 3,  10,   22,   24,     8,     1;
%e A234350 4,  22,   77,  153,   140,    47,      2;
%e A234350 5,  41,  217,  713,  1290,  1112,    322,    15;
%e A234350 7,  72,  530, 2557,  7374, 11743,   8783,  2412,   143,    1;
%e A234350 8, 116, 1149, 7661, 32477, 82988, 116154, 77690, 19621, 1220, 5;
%e A234350 ...
%e A234350 There are e.g. T(8, 11) = 5 non-equivalent ways to arrange 11 indistinguishable points (X) on a triangular grid of side 8 so that no point triple is collinear. As examples of the 5 solutions the 2 symmetrical ones are shown.
%e A234350           .                    .
%e A234350          . .                  . .
%e A234350         . X .                . X .
%e A234350        X . . X              X . . X
%e A234350       X . . . X            . X . X .
%e A234350      . . X X . .          X . . . . X
%e A234350     . X . . . X .        . . X . X . .
%e A234350    . . X . . X . .      . . X . . X . .
%Y A234350 Cf. A194136
%Y A234350 Row lengths are given by A234349
%Y A234350 Column 1 is A001399
%Y A234350 Column 2 is A227327 for n >= 2
%Y A234350 Column 3 is A234351
%Y A234350 Column 4 is A234352
%Y A234350 Column 5 is A234353
%Y A234350 Column 6 is A234354.
%K A234350 nonn,tabf,nice
%O A234350 1,5
%A A234350 _Heinrich Ludwig_, Dec 24 2013