OFFSET
0,3
COMMENTS
Conjectures from Barker confirmed by later formula. - Ray Chandler, Aug 09 2025
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
Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).
FORMULA
From Colin Barker, Jan 22 2016 and Apr 20 2019: (Start)
a(n) = 111*a(n-1)-1110*a(n-2)+1000*a(n-3) for n>4.
G.f.: (1-110*x+12010*x^2-112000*x^3+100000*x^4) / ((1-x)*(1-10*x)*(1-100*x)).
(End)
a(n) = A138148(n) for n > 1. - Ray Chandler, Aug 09 2025
MATHEMATICA
rule=217; 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]]], {k, 1, rows}] (* Binary Representation of Rows *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 20 2016
STATUS
approved