A231348 Number of triangles after n-th stage in a cellular automaton based in isosceles triangles of two sizes (see Comments lines for precise definition).
0, 1, 3, 7, 11, 15, 23, 33, 41, 45, 53, 65, 81, 91, 111, 133, 149, 153, 161, 173, 189, 201, 225, 253, 285, 295, 315, 343, 383, 405, 449, 495, 527, 531, 539, 551, 567, 579, 603, 631, 663, 675, 699, 731, 779, 807, 863, 923, 987, 997, 1017, 1045, 1085, 1113, 1169, 1233, 1313, 1335, 1379, 1439, 1527, 1573, 1665, 1759, 1823
Offset: 0
Keywords
Examples
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.
Links
- Omar E. Pol, Illustration of the structure after 16 stages
- N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
Comments