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.
We start at stage 0 with no triangles, so a(0) = 0. At stage 1 we add a black triangle, so a(1) = 1. At stage 2 we add two black triangles, so a(2) = 1+2 = 3. At stage 3 we add two black triangles and two gray triangles from the vertices of the master triangle, so a(3) = 3+2+2 = 7. At stage 4 we add four black triangles, so a(4) = 7+4 = 11. At stage 5 we add two black triangles and two gray triangles from the vertices of the master triangle, so a(5) = 11+2+2 = 15. At stage 6 we add four black triangles and four gray triangles, so a(6) = 15+4+4 = 23. At stage 7 we add four black triangles and six gray triangles, so a(7) = 23+4+6 = 33. At stage 8 we add eight black triangles, so a(8) = 33+8 = 41. And so on. Note that always we add both black triangles and gray triangles except if n is a power of 2. In this case at stage 2^k we add only 2^k black triangles, for k >= 0.
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