OFFSET
0,2
LINKS
Robert Price, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
Index entries for linear recurrences with constant coefficients, signature (10,1,-10).
FORMULA
From Colin Barker, Jan 04 2016 and Apr 18 2019: (Start)
a(n) = (-450*(-1)^n+10009*10^n-550)/9900 for n>1.
a(n) = 10*a(n-1)+a(n-2)-10*a(n-3) for n>4.
G.f.: (1+x^3-x^4) / ((1-x)*(1+x)*(1-10*x)).
(End)
a(n) = floor(10009*10^n/9900). - Karl V. Keller, Jr., Oct 17 2021
MATHEMATICA
rule=59; 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 *) mc=Table[catri[[k]][[k]], {k, 1, rows}]; (* Keep only middle cell from each row *) Table[FromDigits[Take[mc, k]], {k, 1, rows}] (* Binary Representation of Middle Column *)
PROG
(Python) print([10009*10**n//9900 for n in range(50)]) # Karl V. Keller, Jr., Oct 18 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 03 2016
STATUS
approved