cp's OEIS Frontend

A234251 Triangle T(n, k) = Number of ways to choose k points from an n X n X n triangular grid so that no three of them form a 2 X 2 X 2 subtriangle. Triangle T read by rows.

%I A234251 #17 Feb 01 2015 05:15:01
%S A234251 1,1,1,3,3,1,6,15,16,6,1,10,45,111,156,120,42,2,1,15,105,439,1191,
%T A234251 2154,2583,1977,885,189,9,1,21,210,1305,5565,17052,38337,63576,77208,
%U A234251 67285,40512,15750,3480,333,9,1,28,378,3240,19620,88590,307362,833228,1779219
%N A234251 Triangle T(n, k) = Number of ways to choose k points from an n X n X n triangular grid so that no three of them form a 2 X 2 X 2 subtriangle. Triangle T read by rows.
%C A234251 n starts from 1. The maximal number of points that can be chosen from a grid of side n, so that no three of them are forming a subtriangle of side 2, is A007980(n - 1). So k ranges from 0 to A007980(n - 1).
%C A234251 Column #2 (k = 1) is A000217.
%C A234251 Column #3 (k = 2) is A050534.
%C A234251 Column #4 (k = 3) is A234250.
%H A234251 Heinrich Ludwig, <a href="/A234251/b234251.txt">Table of n, a(n) for n = 1..133</a>
%e A234251 Triangle begins
%e A234251   1,  1;
%e A234251   1,  3,   3;
%e A234251   1,  6,  15,  16,    6;
%e A234251   1, 10,  45, 111,  156,  120,   42,    2;
%e A234251   1, 15, 105, 439, 1191, 2154, 2583, 1977, 885, 189, 9;
%e A234251   ...
%e A234251 There are no more than T(4, 7) = 2 ways to choose 7 points (X) from a 4 X 4 X 4 grid so that no 3 of them form a 2 X 2 X 2 subtriangle:
%e A234251         X              X
%e A234251        X .            . X
%e A234251       . X X          X X .
%e A234251      X X . X        X . X X
%Y A234251 Cf. A000217, A050534, A234250.
%K A234251 nonn,tabf
%O A234251 1,4
%A A234251 _Heinrich Ludwig_, Feb 06 2014