|
|
A266873
|
|
Decimal representation of the n-th iteration of the "Rule 77" elementary cellular automaton starting with a single ON (black) cell.
|
|
2
|
|
|
1, 2, 21, 42, 341, 682, 5461, 10922, 87381, 174762, 1398101, 2796202, 22369621, 44739242, 357913941, 715827882, 5726623061, 11453246122, 91625968981, 183251937962, 1466015503701, 2932031007402, 23456248059221, 46912496118442, 375299968947541, 750599937895082
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|