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 05 2016 and Apr 18 2019: (Start)
a(n) = ((-1)^n + 3*2^(2*n+1) + (-1)^n*2^(2*n+1) - 3)/6.
a(n) = 17*a(n-2) - 16*a(n-4) for n>3.
G.f.: (1+2*x)*(1+4*x^2) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).
(End)
MATHEMATICA
rule=77; 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]], 2], {k, 1, rows}] (* Decimal Representation of Rows *)
PROG
(PARI) a(n) = 4<<(n<<1 - bitand(n, 1)) \ 3; \\ Kevin Ryde, Mar 10 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 04 2016
STATUS
approved