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A266302 Decimal representation of the n-th iteration of the "Rule 15" elementary cellular automaton starting with a single ON (black) cell. 2
1, 6, 1, 126, 1, 2046, 1, 32766, 1, 524286, 1, 8388606, 1, 134217726, 1, 2147483646, 1, 34359738366, 1, 549755813886, 1, 8796093022206, 1, 140737488355326, 1, 2251799813685246, 1, 36028797018963966, 1, 576460752303423486, 1, 9223372036854775806, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
REFERENCES
Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
LINKS
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
FORMULA
From Colin Barker, Dec 28 2015 and Apr 15 2019: (Start)
a(n) = (3*(-1)^n+2^(2*n+1)-(-1)^n*2^(2*n+1)-1)/2.
a(n) = 17*a(n-2)-16*a(n-4) for n>3.
G.f.: (1+6*x-16*x^2+24*x^3) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).
(End)
a(n) = 2*4^n - 2 for odd n; a(n) = 1 for even n. - Karl V. Keller, Jr., Aug 31 2021
E.g.f.: cosh(x) - 2*sinh(x) + 2*sinh(4*x). - Stefano Spezia, Sep 01 2021
MATHEMATICA
rule=15; 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([2*4**n - 2 if n%2 else 1 for n in range(50)]) # Karl V. Keller, Jr., Aug 31 2021
CROSSREFS
Sequence in context: A331557 A352058 A303675 * A352012 A183284 A224476
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 26 2015
STATUS
approved

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Last modified April 18 22:18 EDT 2024. Contains 371782 sequences. (Running on oeis4.)