A266255 Decimal representation of the n-th iteration of the "Rule 11" elementary cellular automaton starting with a single ON (black) cell.
1, 4, 3, 124, 3, 2044, 3, 32764, 3, 524284, 3, 8388604, 3, 134217724, 3, 2147483644, 3, 34359738364, 3, 549755813884, 3, 8796093022204, 3, 140737488355324, 3, 2251799813685244, 3, 36028797018963964, 3, 576460752303423484, 3, 9223372036854775804, 3
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..999
- Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
- Index entries for sequences related to cellular automata
- Index to Elementary Cellular Automata
Programs
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Mathematica
rule=11; 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[FromDigits[catri[[k]],2],{k,1,rows}] (* Decimal Representation of Rows *) -
Python
print([2*4**n - 4 if n%2 else 3 - 2*0**n for n in range(33)]) # Karl V. Keller, Jr., Aug 26 2021
Formula
From Colin Barker, Dec 27 2015 and Apr 14 2019: (Start)
a(n) = (7*(-1)^n+2^(2*n+1)-(-1)^n*2^(2*n+1)-1)/2 for n>0.
a(n) = 17*a(n-2)-16*a(n-4) for n>4.
G.f.: (1+4*x-14*x^2+56*x^3-32*x^4) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).
(End)
a(n) = 2*4^n - 4 for odd n; a(n) = 3 - 2*0^n for even n. - Karl V. Keller, Jr., Aug 26 2021
Comments