This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
For m = 1 the unique solution is 1 + 2 = 3. For m = 4 there are 8 solutions: 1 5 6 | 1 5 6 | 2 5 7 | 1 6 7 2 8 10 | 3 7 10 | 3 6 9 | 4 5 9 4 7 11 | 2 9 11 | 1 10 11 | 3 8 11 3 9 12 | 4 8 12 | 4 8 12 | 2 10 12 --------+---------+---------+-------- 2 4 6 | 2 6 8 | 3 4 7 | 3 5 8 1 9 10 | 4 5 9 | 1 8 9 | 2 7 9 3 8 11 | 3 7 10 | 5 6 11 | 4 6 10 5 7 12 | 1 11 12 | 2 10 12 | 1 11 12 . The 8 solutions for m = 4, one per line: (1, 5, 6), (2, 8, 10), (3, 9, 12), (4, 7, 11); (1, 5, 6), (2, 9, 11), (3, 7, 10), (4, 8, 12); (1, 10, 11), (2, 5, 7), (3, 6, 9), (4, 8, 12); (1, 6, 7), (2, 10, 12), (3, 8, 11), (4, 5, 9); (1, 9, 10), (2, 4, 6), (3, 8, 11), (5, 7, 12); (1, 11, 12), (2, 6, 8), (3, 7, 10), (4, 5, 9); (1, 8, 9), (2, 10, 12), (3, 4, 7), (5, 6, 11); (1, 11, 12), (2, 7, 9), (3, 5, 8), (4, 6, 10).
Table[Length[Select[Subsets[Select[Subsets[Range[3 n], {3}], #[[1]] + #[[2]] == #[[3]] &], {n}], Range[3 n] == Sort[Flatten[#]] &]], {n, 0,
5}] (* Suitable only for n<6. See Knuth's Dancing Links algorithm for n>5. *) (* Robert Price, Apr 03 2019 *)
A = lambda n:sum(1 for t in DLXCPP([(a-1,b-1,a+b-1) for a in (1..3*n) for b in (1..min(3*n-a,a-1))])) # Tomas Boothby, Oct 11 2013
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