OFFSET
1,2
COMMENTS
This gives the number of edge segments that are distinct with respect to rotation and mirror images. Sequence is arranged so that j <= k (since 2 X 3 and 3 X 2 are equivalent grids), first by increasing j, then by increasing k: a(1) = 1 X 1 = 1, a(2) = 1 X 2 = 2, a(3) = 2 X 2 = 1, a(4) = 1 X 3 = 3.
LINKS
Doug Bell, Table of n, a(n) for n = 1..11325, Rows n = 1..150, flattened.
EXAMPLE
Triangle begins:
1;
2, 1;
3, 3, 2;
3, 3, 4, 2;
4, 4, 5, 5, 3;
4, 4, 5, 5, 6, 3;
5, 5, 6, 6, 7, 7, 4;
...
For n = 9, the a(9) = 4 distinct edge segments [A,B,C,D] for a 3 X 4 rectangular grid are:
+ - - - - + + A B B A +
| | C C
| | --> D D
| | C C
+ - - - - + + A B B A +.
MATHEMATICA
Table[Ceiling[j/2] + Boole[j != k] Ceiling[k/2], {j, 14}, {k, j}] // Flatten (* Michael De Vlieger, Jun 09 2017 *)
CROSSREFS
AUTHOR
Doug Bell, May 28 2017
STATUS
approved