A350632 a(n) is the total number of ON cells at stage n of a cellular automaton where cells are turned ON when they have one or two neighbors ON (see Comments for precise definition).

0, 1, 9, 21, 45, 57, 85, 121, 177, 189, 217, 253, 329, 373, 465, 557, 721, 737, 765, 801, 877, 921, 1013, 1105, 1301, 1377, 1485, 1601, 1805, 1985, 2221, 2449, 2873, 2909, 2937, 2973, 3049, 3093, 3185, 3277, 3473, 3549, 3657, 3773, 3977, 4157, 4393, 4621, 5113

Offset: 0

Author

Rémy Sigrist, Jan 08 2022

Keywords

• nonn

Comments

On the infinite square grid, start with all cells OFF.

Turn a single cell to the ON state.

At each subsequent step, each cell with exactly one or two neighbors ON is turned ON, and everything that is already ON remains ON.

Here "neighbor" refers to the eight adjacent and diagonally adjacent cells in the Moore neighborhood.

Examples

			The first 5 generations can be depicted as follows:
         . . . . . . . . . . .
         . 5 5 . . . . . 5 5 .
         . 5 4 4 4 4 4 4 4 5 .
         . . 4 3 3 . 3 3 4 . .
         . . 4 3 2 2 2 3 4 . .
         . . 4 . 2 1 2 . 4 . .
         . . 4 3 2 2 2 3 4 . .
         . . 4 3 3 . 3 3 4 . .
         . 5 4 4 4 4 4 4 4 5 .
         . 5 5 . . . . . 5 5 .
         . . . . . . . . . . .
- so a(0) = 0,
     a(1) = 0 + 1 = 1,
     a(2) = 1 + 8 = 9,
     a(3) = 9 + 12 = 21,
     a(4) = 21 + 24 = 45,
     a(5) = 45 + 12 = 57.
		

Links

• Rémy Sigrist, Log periodic coloring of the structure at stage 512
• Rémy Sigrist, C++ program for A350632
• Index entries for sequences related to cellular automata

Crossrefs

Cf. A147562, A151725, A160414, A256530, A350633, A350639.