A330283 -id:A330283 - cp's OEIS frontend

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

Robert Munafo

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

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

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

Cf. A056613, A056614, A056605, A330283.

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

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

Original entry on oeis.org

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

N. J. A. Sloane, Aug 28 2000

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

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

S. Ekström, Enumerating Still Lifes (in C)
Mark D. Niemiec, Life Object Counts

Cf. A019473, A330283.

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

cp's OEIS Frontend

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

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