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

0,1

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.

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.)

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

Example

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

Crossrefs

Cf. A097981, A151725, A151731.

Sequence in context: A236475 A287458 A050572 * A105343 A237834 A147955

Adjacent sequences: A249665 A249666 A249667 * A249669 A249670 A249671

Keyword

nonn

Author

Eric M. Schmidt, Nov 03 2014

Status

approved