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

0,3

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.

Links

Table of n, a(n) for n=0..48.

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

Example

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.

Prog

(C++) See Links section.

Crossrefs

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

Sequence in context: A110680 A163205 A154862 * A020137 A231570 A020190

Adjacent sequences: A350629 A350630 A350631 * A350633 A350634 A350635

Keyword

nonn

Author

Rémy Sigrist, Jan 08 2022

Status

approved