A019473 Number of stable n-celled patterns ("still lifes") in Conway's Game of Life, up to rotation and reflection.

0, 0, 0, 2, 1, 5, 4, 9, 10, 25, 46, 121, 240, 619, 1353, 3286, 7773, 19044, 45759, 112243, 273188, 672172, 1646147, 4051732, 9971377, 24619307, 60823008, 150613157, 373188952, 926068847, 2299616637, 5716948683, 14223867298, 35422864104

Offset

1,4

Comments

This sequence only counts still lifes that cannot be broken down into 2 or more smaller still lifes. That is, it only counts "strict" still lifes (contrast with A056613). - Nathaniel Johnston, Dec 11 2019

Links

Table of n, a(n) for n=1..34.

S. Ekström, Enumerating Still Lifes (in C)

N. D. Elkies, The still-Life density problem and its generalizations, arXiv:math/9905194 [math.CO], 1999.

H. Koenig, Stable Objects (another version of this sequence)

R. Munafo, Still-Lifes with N cells in Conway's game of Life

Mark D. Niemiec, Life Object Counts

R. C. Schroeppel, A few mathematical experiments

Eric Weisstein's World of Mathematics, Game of Life

Example

a(4)=2 because the block and the tub are the only 4-cell still lifes.

Crossrefs

Cf. A056613, A056614, A056605, A330283.

Sequence in context: A325771 A207480 A166517 * A056605 A091802 A144240

Adjacent sequences: A019470 A019471 A019472 * A019474 A019475 A019476

Keyword

hard,nonn,nice

Author

Robert Munafo

Extensions

More terms from Stephen A. Silver, Dec 11 1999

a(24) corrected, at the suggestion of Mark Niemiec, by Nathaniel Johnston, Aug 26 2016

a(24)-a(28) corrected, using data computed by Simon Ekström, by Adam P. Goucher, Jan 08 2017

a(31)-a(32) from Nathaniel Johnston, using a script made by Simon Ekström, May 25 2017

a(33) from Nathaniel Johnston, using a script made by Simon Ekström, Apr 05 2019

a(34) from Nathaniel Johnston, using a script made by Simon Ekström, Jan 09 2020

Status

approved