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A262861
Binary representation of the n-th iteration of the "Rule 147" elementary cellular automaton starting with a single ON (black) cell.
2
1, 101, 10001, 1011101, 100010001, 10111011101, 1000100010001, 101110111011101, 10001000100010001, 1011101110111011101, 100010001000100010001, 10111011101110111011101, 1000100010001000100010001, 101110111011101110111011101, 10001000100010001000100010001
OFFSET
0,2
FORMULA
From Colin Barker, Jan 17 2016 and Apr 17 2019: (Start)
a(n) = 10001*a(n-2) - 10000*a(n-4) for n>3.
G.f.: (1+101*x+1000*x^3) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).
(End)
a(n) = floor((10000 + 110*(n mod 2))*100^n/9999). - Karl V. Keller, Jr., Aug 11 2021
MATHEMATICA
rule=147; 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([(10000 + 110*(n%2))*100**n//9999 for n in range(30)]) # Karl V. Keller, Jr., Aug 11 2021
CROSSREFS
Sequence in context: A152756 A265172 A153500 * A371563 A164367 A263244
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 17 2016
STATUS
approved