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%I #18 Mar 23 2020 19:16:13
%S 1,1,1,1,1,1,1,2,4,6,4,2,1,1,3,10,25,41,48,41,25,10,3,1,1,4,22,87,244,
%T 526,870,1110,1110,870,526,244,87,22,4,1,1,5,41,238,1029,3450,9147,
%U 19524,34104,49231,59038,59038,49231,34104,19524,9147,3450,1029,238
%N Triangle T(n, k) read by rows giving number of non-equivalent ways to choose k points in an equilateral triangle grid of side n.
%C Number of orbits under dihedral group D_6 of order 6. - _N. J. A. Sloane_, Sep 12 2019
%H Heinrich Ludwig, <a href="/A231655/b231655.txt">Table of n, a(n) for n = 0..173</a>
%e Triangle T(n, k) is irregularly shaped: 0 <= k <= n*(n+1)/2+1. The first row corresponds to n = 1, the first column corresponds to k = 0. Rows are palindromic.
%e 1, 1;
%e 1, 1, 1, 1;
%e 1, 2, 4, 6, 4, 2, 1;
%e 1, 3, 10, 25, 41, 48, 41, 25, 10, 3, 1;
%e ...
%e There are T(3, 2) = 4 nonisomorphic choices of 2 points (X) in an equilateral triangle grid of side 3:
%e X . . X
%e . . X X . . X .
%e . X . . . . X . X . . .
%Y Columns k=1..5 are A001399, A227327, A230723, A231653, A231654.
%Y Cf. A054252, A283113, A289709, A326611.
%K nonn,tabf
%O 0,8
%A _Heinrich Ludwig_, Nov 14 2013
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