OFFSET
0,2
COMMENTS
Rule 43 also generates 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
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
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 25 2015
STATUS
approved