A231655 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.

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, 526, 870, 1110, 1110, 870, 526, 244, 87, 22, 4, 1, 1, 5, 41, 238, 1029, 3450, 9147, 19524, 34104, 49231, 59038, 59038, 49231, 34104, 19524, 9147, 3450, 1029, 238

Offset: 0

Author

Heinrich Ludwig, Nov 14 2013

Keywords

• nonn
• tabf

Comments

Number of orbits under dihedral group D_6 of order 6. - N. J. A. Sloane, Sep 12 2019

Examples

			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.
  1,  1;
  1,  1,  1,  1;
  1,  2,  4,  6,  4,  2,  1;
  1,  3, 10, 25, 41, 48, 41, 25, 10,  3,  1;
  ...
There are T(3, 2) = 4 nonisomorphic choices of 2 points (X) in an equilateral triangle grid of side 3:
      X       .       .       X
     . .     X X     . .     X .
    . X .   . . .   X . X   . . .
		

Links

• Heinrich Ludwig, Table of n, a(n) for n = 0..173

Crossrefs

Columns k=1..5 are A001399, A227327, A230723, A231653, A231654.

Cf. A054252, A283113, A289709, A326611.