cp's OEIS Frontend

A243211 Triangle T(n, k) = Numbers of ways to place k points on a triangular grid of side n so that no three of them are vertices of an equilateral triangle with sides parallel to the grid. Triangle read by rows.

%I A243211 #9 Jun 13 2014 12:04:08
%S A243211 1,1,1,3,3,1,6,15,15,3,1,10,45,107,128,63,10,1,15,105,428,1062,1566,
%T A243211 1276,507,69,1,21,210,1282,5160,13971,25191,29235,20508,7747,1251,42,
%U A243211 1,1,28,378,3198,18591,77124,231090,498097,759117,792942,540361,222597,49053
%N A243211 Triangle T(n, k) = Numbers of ways to place k points on a triangular grid of side n so that no three of them are vertices of an equilateral triangle with sides parallel to the grid. Triangle read by rows.
%C A243211 The triangle T(n, k) is irregularly shaped: 0 <= k <= A227308(n). First row corresponds to n = 1.
%C A243211 The maximal number of points that can be placed on a triangular grid of side n so that no three of them form an equilateral triangle with sides parallel to the grid is given by A227308(n).
%H A243211 Heinrich Ludwig, <a href="/A243211/b243211.txt">Table of n, a(n) for n = 1..165</a>
%e A243211 The triangle begins:
%e A243211   1,  1;
%e A243211   1,  3,   3;
%e A243211   1,  6,  15,   15,    3;
%e A243211   1, 10,  45,  107,  128,    63,    10,
%e A243211   1, 15, 105,  428, 1062,  1566,  1276,   507,    69,
%e A243211   1, 21, 210, 1282, 5160, 13971, 25191, 29235, 20508, 7747, 1251, 42, 1;
%e A243211   ...
%e A243211 There is T(6, 12) = 1 way to place 12 points (x) on the grid obeying the rule in the definition of the sequence:
%e A243211            .
%e A243211           x x
%e A243211          x . x
%e A243211         x . . x
%e A243211        x . . . x
%e A243211       . x x x x .
%Y A243211 Cf. A227308, A243207, A084546, A234251, A239567, A240439, A194136, A000217 (column 2), A050534 (column 3), A243212 (column 4), A243213 (column 5), A243214 (column 6).
%K A243211 nonn,tabf
%O A243211 1,4
%A A243211 _Heinrich Ludwig_, Jun 09 2014