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A266245
Decimal representation of the n-th iteration of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell.
2
1, 0, 5, 96, 29, 1952, 29, 32672, 29, 524192, 29, 8388512, 29, 134217632, 29, 2147483552, 29, 34359738272, 29, 549755813792, 29, 8796093022112, 29, 140737488355232, 29, 2251799813685152, 29, 36028797018963872, 29, 576460752303423392, 29, 9223372036854775712
OFFSET
0,3
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
From Colin Barker, Dec 28 2015 and Apr 14 2019: (Start)
a(n) = 17*a(n-2)-16*a(n-4) for n>7.
G.f.: (1-12*x^2+96*x^3-40*x^4+320*x^5-384*x^6+1024*x^7) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).
(End)
a(n) = 4^n/2 + 90*floor(4^n/60) - 90 for odd n>3; a(n) = 29 for even n>3. - Karl V. Keller, Jr., Aug 17 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 *) Table[FromDigits[catri[[k]], 2], {k, 1, rows}] (* Decimal Representation of Rows *)
PROG
(Python) print([1, 0, 5, 96]+[4**n//2 + 90*(4**n//60) - 90 if n%2 else 29 for n in range(4, 50)]) # Karl V. Keller, Jr., Aug 17 2021
CROSSREFS
Sequence in context: A218463 A192343 A152839 * A194616 A285367 A208253
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 25 2015
STATUS
approved