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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 Robert Price, Table of n, a(n) for n = 0..999 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton Index entries for sequences related to cellular automata Index to Elementary Cellular Automata Index entries for linear recurrences with constant coefficients, signature (0,17,0,-16). 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 Cf. A266300, A266301. Sequence in context: A331557 A352058 A303675 * A352012 A183284 A224476 Adjacent sequences: A266299 A266300 A266301 * A266303 A266304 A266305 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.)