login
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.
4
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
0,8
COMMENTS
Number of orbits under dihedral group D_6 of order 6. - N. J. A. Sloane, Sep 12 2019
LINKS
EXAMPLE
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 . . .
CROSSREFS
Columns k=1..5 are A001399, A227327, A230723, A231653, A231654.
Sequence in context: A339671 A367198 A317310 * A018841 A182043 A337937
KEYWORD
nonn,tabf
AUTHOR
Heinrich Ludwig, Nov 14 2013
STATUS
approved