A319159 Given an equilateral triangular grid with side n, containing n(n+1)/2 points, a(n) is the minimal number of points to be selected, such that any equilateral triangle of points will include at least one of the selection.
1, 2, 4, 7, 11, 16, 22, 28, 35, 44, 53, 63, 74, 86
Offset: 1
Examples
For n=4, this sequence has the same value a(4)=4 as A227116 and A319158, but if we look at the three solutions to those sequences (unique up to symmetry), representing selected points by O:
O O O
O , . , . .
, . O , O . . O .
. O , . O . , O . O O .
We see that only the last of these is a solution here -- the others have rotated triangles not including any selected point (for example, as shown with commas). The last selection is therefore the unique solution (up to symmetry) for a(4)=4.
Links
- Ed Wynn, A comparison of encodings for cardinality constraints in a SAT solver, arXiv:1810.12975 [cs.LO], 2018.
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