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

%I A038185 #13 Feb 16 2025 08:32:38
%S A038185 1,3,5,13,17,59,81,219,257,899,1349,3437,4353,15235,20805,56173,65537,
%T A038185 229379,344069,876557,1118225,3913787,5313617,14399195,16842753,
%U A038185 58949635,88424453,225271821,285282321
%N A038185 One-dimensional cellular automaton 'sigma' (Rule 150).
%C A038185 Generation n (starting from the generation 0: 1) cut after the central 1-column and interpreted as a binary number.
%C A038185 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
%H A038185 N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168 [math.CO], 2015
%H A038185 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A038185 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A038185 Wolfram Research, <a href="http://atlas.wolfram.com/">Wolfram Atlas of Simple Programs</a>
%H A038185 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A038185 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A038185 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%p A038185 bit_n := (x,n) -> `mod`(floor(x/(2^n)),2);
%p A038185 sigmacut := proc(n): if (0 = n) then (1)
%p A038185 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:
%Y A038185 Cf. A006977, A006978, A038183, a(n) = floor(A038184[ n ]/2^n)
%K A038185 nonn
%O A038185 0,2
%A A038185 Antti Karttunen, Feb 09 1999