A038185 One-dimensional cellular automaton 'sigma' (Rule 150).

1, 3, 5, 13, 17, 59, 81, 219, 257, 899, 1349, 3437, 4353, 15235, 20805, 56173, 65537, 229379, 344069, 876557, 1118225, 3913787, 5313617, 14399195, 16842753, 58949635, 88424453, 225271821, 285282321

Offset: 0

Author

Antti Karttunen, Feb 09 1999

Keywords

• nonn

Comments

Generation n (starting from the generation 0: 1) cut after the central 1-column and interpreted as a binary number.

Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 518", based on the 5-celled von Neumann neighborhood. Initialized with a single black (ON) cell at stage zero. - Robert Price, Feb 22 2017

Links

• N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015
• Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
• S. Wolfram, A New Kind of Science
• Wolfram Research, Wolfram Atlas of Simple Programs
• Index to 2D 5-Neighbor Cellular Automata
• Index to Elementary Cellular Automata
• Index entries for sequences related to cellular automata

Crossrefs

Cf. A006977, A006978, A038183, a(n) = floor(A038184[ n ]/2^n)

Programs

Maple

bit_n := (x,n) -> `mod`(floor(x/(2^n)),2);
sigmacut := proc(n): if (0 = n) then (1)
else sum('((bit_n(sigmagen(n-1),i+1+n-1)+bit_n(sigmagen(n-1),i+n-1)+bit_n(sigmagen(n-1),i-1+n-1)) mod 2)*(2^i)', 'i'=0..(n)) fi: end: