A056613 Number of n-celled pseudo still lifes in Conway's Game of Life, up to rotation and reflection.

0, 0, 0, 0, 0, 0, 0, 1, 1, 7, 16, 55, 110, 279, 620, 1645, 4067, 10843, 27250, 70637, 179011, 462086, 1184882, 3069135, 7906676, 20463274, 52816265, 136655095, 353198379, 914075620, 2364815358, 6123084116, 15851861075, 41058173683

Offset

1,10

Comments

There are two slightly different possible definitions for a pseudo still life: a still life that can be partitioned into exactly two different still lifes, or a still life that can be partitioned into two *or more* still lifes. This sequence uses the latter definition. The first point in the sequence where this makes a difference is a(32) = 6123084116, which would be a(32) = 6123084115 under the former definition. - Nathaniel Johnston, May 25 2017

Links

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

S. Ekström, Enumerating Still Lifes (in C)

Mark D. Niemiec, Life Object Counts

Example

For n = 8, the unique pseudo still life is a pair of 2 X 2 blocks occupying a 5 X 2 bounding box.

Crossrefs

Cf. A019473, A330283.

Sequence in context: A065099 A001345 A225128 * A318413 A342873 A183343

Adjacent sequences: A056610 A056611 A056612 * A056614 A056615 A056616

Keyword

nonn,hard,more

Author

N. J. A. Sloane, Aug 28 2000

Extensions

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

a(25)-a(30) computed by Simon Ekström and inserted by Adam P. Goucher, Jan 08 2017

a(24) corrected by Nathaniel Johnston, Feb 21 2017 (computed by Simon Ekström)

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