cp's OEIS Frontend

A243207 Triangle T(n, k) = Numbers of inequivalent (mod D_3) 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 A243207 #9 Jun 03 2014 02:31:32
%S A243207 1,1,1,2,4,3,1,3,10,20,25,11,3,4,22,77,186,266,221,86,14,5,41,223,881,
%T A243207 2344,4238,4885,3451,1296,220,7,1,7,72,552,3146,12907,38640,83107,
%U A243207 126701,132236,90214,37128,8235,775,24,8,116,1196,9264,53307,232861,773930
%N A243207 Triangle T(n, k) = Numbers of inequivalent (mod D_3) 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 A243207 The triangle T(n, k) is irregularly shaped: 1 <= k <= A227308(n). First row corresponds to n = 1.
%C A243207 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 A243207 Heinrich Ludwig, <a href="/A243207/b243207.txt">Table of n, a(n) for n = 1..153</a>
%e A243207 The triangle begins:
%e A243207   1;
%e A243207   1,  1;
%e A243207   2,  4,   3,   1;
%e A243207   3, 10,  20,  25,   11,    3;
%e A243207   4, 22,  77, 186,  266,  221,   86,   14;
%e A243207   5, 41, 223, 881, 2344, 4238, 4885, 3451, 1296, 220, 7, 1;
%e A243207   ...
%e A243207 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 A243207            .
%e A243207           x x
%e A243207          x . x
%e A243207         x . . x
%e A243207        x . . . x
%e A243207       . x x x x .
%Y A243207 Cf. A227308, A243211, A239572, A234247, A231655, A243141, A001399 (column 1), A227327 (column 2), A243208 (column 3), A243209 (column 4), A243210 (column 5).
%K A243207 tabf,nonn
%O A243207 1,4
%A A243207 _Heinrich Ludwig_, Jun 01 2014