OFFSET
0,2
COMMENTS
Rules 38,134 and 166 also generate this sequence.
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
S. Wolfram, A New Kind of Science
Index entries for linear recurrences with constant coefficients, signature (0, 10000).
FORMULA
From Colin Barker, Dec 23 2015 and Apr 13 2019: (Start)
a(n) = 4^(n-1)*5^(2*n-1)*(21-(-1)^n).
a(n) = 10000*a(n-2) for n>1.
G.f.: (1+110*x) / ((1-100*x)*(1+100*x)). (End)
a(n) = 110*100^(n-1) for odd n; a(n) = 100^n for even n. - Karl V. Keller, Jr., Aug 11 2021
MATHEMATICA
rule=6; 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]]], {k, 1, rows}] (* Binary Representation of Rows *)
PROG
(Python) print([110*100**(n-1) if n%2 else 100**n for n in range(30)]) # Karl V. Keller, Jr., Aug 11 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 22 2015
STATUS
approved