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..500
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
S. Wolfram, A New Kind of Science
FORMULA
Conjectured g.f.: (-(1 + x)^(-2) + (-3 + 3*x - 2*x^2)/(-1 + x)^3)/2. - Michael De Vlieger, Dec 29 2015
Conjectures from Colin Barker, Dec 30 2015 and Apr 15 2019: (Start)
a(n) = (n^2+2*n-(-1)^n*(n+1)+3)/2.
a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>4.
(End)
MATHEMATICA
rule=23; 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 *) Table[Total[Take[nbc, k]], {k, 1, rows}] (* Number of Black cells through stage n *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 29 2015
STATUS
approved