A298819 a(n) is the period of the oscillating pattern formed by a 1 X n line of cells in the Life-like cellular automaton B2c3-cekq4ikt5i8/S2-in3-acky4aijry5eiky6i, or 0 if the pattern vanishes.

0, 0, 2, 2, 2, 0, 6, 6, 12, 4, 28, 14, 14, 0, 14, 14, 84, 12, 372, 62, 248, 8, 504, 126, 252, 28, 420, 30, 30, 0, 30, 30, 420, 28, 2044, 1022, 12264, 24, 504, 126, 7812, 124, 253828, 4094, 32752, 16, 16368, 2046, 85932, 252, 18396, 1022, 4088, 56, 917448, 32766, 327660, 60, 1860, 62, 62, 0, 62, 62

Offset: 1

Author

WG Zeist, Jan 26 2018

Keywords

• nonn

Comments

An explanation of the Hensel notation used to define the cellular automaton rule can be found on the LifeWiki (see links).

Examples

			a(4) = 2 because a 1 X 4 line oscillates with period 2 in this cellular automaton.
		

Links

• LifeWiki, Isotropic non-totalistic Life-like cellular automaton

Crossrefs

Cf. A000918, A003558, A160657, A268754.

Formula

For n divisible by 4, a(n) = A160657(n/4) = (a divisor of) 2^(A003558(n/4) + 1) - 2.

With the exception of a(1), all values of n for which a(n) = 0 are of the form 2^m - 2 for some integer m (A000918).

a(2k) = A268754(k); a(2k+1) = lcm(A268754(k), A268754(k+1)) (conjectured). Note that, by an arbitrary/cosmetic convention, A268754 uses 1 for empty patterns and A298819 uses 0. - WG Zeist and Charlie Neder, Jan 11 2019