OFFSET
0,2
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
A. J. Macfarlane, Generating functions for integer sequences defined by the evolution of cellular automata..., Fig. 16
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
S. Wolfram, A New Kind of Science
FORMULA
Conjectures from Colin Barker, Jan 23 2016 and Apr 20 2019: (Start)
a(n) = a(n-1)+16*a(n-2)-16*a(n-3) for n>2.
G.f.: (1+6*x) / ((1-x)*(1-4*x)*(1+4*x)).
(End)
Empirical a(n) = (25*4^n-3*(-4)^n-7)/15. - Colin Barker, Nov 25 2016 and Apr 20 2019
MATHEMATICA
rule=246; 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 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 22 2016
STATUS
approved