A179415 The number of alive cells in Conway's Game of Life on the infinite square grid, in the "lumps of muck" sequence of patterns leading from the grandfather of "stairstep hexomino" to a stable configuration of four blocks, known as a blockade.

6, 6, 6, 8, 10, 12, 16, 18, 20, 26, 24, 28, 30, 22, 32, 28, 32, 36, 48, 42, 56, 34, 26, 28, 40, 38, 50, 48, 46, 64, 48, 46, 48, 46, 48, 56, 52, 66, 62, 66, 68, 86, 60, 70, 64, 72, 50, 50, 50, 40, 42, 46, 48, 36, 38, 36, 42, 48, 46, 44, 34, 30, 26, 22, 20, 16, 16, 16, 16, 16

Offset

0,1

Comments

For n >= 65, a(n)=16. Note that the same history is traced on any toroidal grid with size at least 26 X 26.

All terms are even because the initial pattern has an even number of cells and because it has 180-degree rotational symmetry.

Links

Table of n, a(n) for n=0..69.

Antti Karttunen, J-program for computing the terms of this sequence

Stephen A. Silver, Life Lexicon, "lumps of muck"

Example

The generations 0-3 of this cycle of patterns look as follows, thus a(0)=a(1)=a(2)=6 and a(3)=8.
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..................................|stairstep hexomino................
Generations 4-7 of this cycle of patterns look as follows, thus a(4)=10, a(5)=12, a(6)=16 and a(7)=18.
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.(handshake). . | . . . . . . . . | . . . . . . . . | . . . . . . . .
At generation 65, the following stable formation of four blocks is reached, called "blockade", and thus for n >= 65, a(n)=16.
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Crossrefs

A179409, which traces the history of the same initial pattern on an 8 X 8 toroidal grid, differs from this one for the first time at n=14, as a(14)=32, while A179409(14)=26.

Sequence in context: A322346 A332559 A361871 * A179409 A186983 A046264

Adjacent sequences: A179412 A179413 A179414 * A179416 A179417 A179418

Keyword

nonn

Author

Antti Karttunen, Jul 27 2010

Status

approved