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 16 2016: (Start)
a(n) = (2*n^2+12*n-(-1)^n-7)/4 for n>0.
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>4.
G.f.: 2*x*(1+x-x^3) / ((1-x)^3*(1+x)).
(End)
MATHEMATICA
rule=133; 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 *) nbc=Table[Total[catri[[k]]], {k, 1, rows}]; (* Number of Black cells in stage n *) nwc=Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}]; (* Number of White cells in stage n *) Table[Total[Take[nwc, k]], {k, 1, rows}] (* Number of White cells through stage n *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Price, Jan 15 2016
STATUS
approved