OFFSET
0,3
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
LINKS
Robert Price, Table of n, a(n) for n = 0..499
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
FORMULA
Conjectures from Colin Barker, Dec 26 2015 and Apr 14 2019: (Start)
a(n) = 1/2*(n+1)*(n+(-1)^n+1) for n>0.
a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>5.
G.f.: x*(1+5*x-2*x^2-x^3+x^4) / ((1-x)^3*(1+x)^2).
(End)
MATHEMATICA
rule=7; 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,easy
AUTHOR
Robert Price, Dec 24 2015
EXTENSIONS
Conjectures from Colin Barker, Apr 14 2019
STATUS
approved