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

Author

Robert Munafo

Keywords

• hard
• nonn
• nice

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

Examples

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

Links

• 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

Crossrefs

Cf. A056613, A056614, A056605, A330283.

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