A267445 Number of ON (black) cells in the n-th iteration of the "Rule 129" elementary cellular automaton starting with a single ON (black) cell.
1, 0, 1, 0, 5, 3, 5, 0, 13, 11, 13, 7, 17, 11, 13, 0, 29, 27, 29, 23, 33, 27, 29, 15, 41, 35, 37, 23, 41, 27, 29, 0, 61, 59, 61, 55, 65, 59, 61, 47, 73, 67, 69, 55, 73, 59, 61, 31, 89, 83, 85, 71, 89, 75, 77, 47, 97, 83, 85, 55, 89, 59, 61, 0, 125, 123, 125
Offset: 0
References
- S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
Links
- Robert Price, Table of n, a(n) for n = 0..1000
- Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
- S. Wolfram, A New Kind of Science
- Index entries for sequences related to cellular automata
- Index to Elementary Cellular Automata
Crossrefs
Cf. A267417.
Programs
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Mathematica
rule=129; rows=20; ca=CellularAutomaton[rule,{{1},0},rows-1,{All,All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]],{rows-k+1,rows+k-1}],{k,1,rows}]; (* Truncated list of each row *) Table[Total[catri[[k]]],{k,1,rows}] (* Number of Black cells in stage n *)
Formula
Conjecture: a(n) = A071050(n), n>0. - R. J. Mathar, Jan 17 2016