OFFSET
0,2
REFERENCES
Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
LINKS
Robert Price, Table of n, a(n) for n = 0..999
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
Index entries for linear recurrences with constant coefficients, signature (2,1,-2).
FORMULA
From Colin Barker, Dec 28 2015 and Apr 14 2019: (Start)
a(n) = (65*2^n-8*((-1)^n+3))/48 for n>3.
a(n) = 2*a(n-1)+a(n-2)-2*a(n-3) for n>6.
G.f.: (1+x^5-x^6) / ((1-x)*(1+x)*(1-2*x)).
(End)
a(n) = floor(65*2^n/48). - Karl V. Keller, Jr., Dec 15 2021
MATHEMATICA
rule=9; 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], 2], {k, 1, rows}] (* Binary Representation of Middle Column *)
PROG
(Python) print([65*2**n//48 for n in range(50)]) # Karl V. Keller, Jr., Dec 15 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 25 2015
STATUS
approved