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
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
S. Wolfram, A New Kind of Science
FORMULA
Conjectures from Colin Barker, Jan 03 2016 and Apr 18 2019: (Start)
a(n) = (-1/2-(-4)^n+(-2)^n+(-1)^n/2+4^n).
G.f.: (1+7*x-3*x^2+8*x^3+32*x^4) / ((1-x)*(1+x)*(1+2*x)*(1-4*x)*(1+4*x)).
(End)
Conjecture: a(n) = 2*4^n - 2^n - 1 for odd n; a(n) = 2^n for even n. - Karl V. Keller, Jr., Oct 12 2021
MATHEMATICA
rule=51; 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
AUTHOR
Robert Price, Jan 02 2016
STATUS
approved