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.
FORMULA
Conjectures from Colin Barker, Jan 01 2016 and Apr 18 2019: (Start)
a(n) = 10101*a(n-2)-1010100*a(n-4)+1000000*a(n-6) for n>7.
G.f.: (1 +10*x -8991*x^2 +898991*x^3 -10091010*x^4 +1009091010*x^5 +10100000*x^6 -1010100000*x^7) / ((1 -x)*(1 +x)*(1 -10*x)*(1 +10*x)*(1 -100*x)*(1 +100*x)).
(End)
Conjecture: a(n) = (10*100^n - 99999*10^(n-2) - 1)/9 for odd n > 1; a(n) = 111*10^(n-1) for even n > 1. - Karl V. Keller, Jr., Oct 06 2021
MATHEMATICA
rule=37; 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 01 2016
STATUS
approved