A249668 Population of the n-th generation of the pattern 101//010 in the Life Without Death cellular automaton.

3, 4, 7, 10, 15, 20, 25, 30, 38, 47, 55, 63, 69, 79, 91, 96, 105, 112, 124, 134, 139, 144, 152, 157, 163, 168, 176, 183, 187, 195, 205, 217, 223, 229, 239, 247, 259, 273, 285, 289, 295, 303, 311, 323, 334, 339, 343, 351, 363, 375, 383, 389, 397, 405, 413, 423

Offset: 0

Author

Eric M. Schmidt, Nov 03 2014

Keywords

• nonn

Comments

Each generation, a cell turns on if it has exactly three neighbors that are on. Cells never turn off.

This pattern grows indefinitely. No other connected 3-celled pattern does so.

Examples

			Generation 0:
101
010
Generation 1:
111
010
Generation 2:
010
111
111
Generation 3:
111
111
111
010
Generation 4:
00100
01110
11111
01110
01110
		

Links

• Eric M. Schmidt, Table of n, a(n) for n = 0..2500
• LifeWiki, Life without death
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1). (Initial terms do not obey recurrence; see formula section.)

Crossrefs

Cf. A097981, A151725, A151731.

Formula

For n >= 2108, a(n+6) = a(n) + 260. - Eric M. Schmidt, Nov 04 2014

For n >= 2115, a(n) = a(n-1) + a(n-6) - a(n-7). - Eric M. Schmidt, Nov 05 2014