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 A266324 Decimal representation of the n-th iteration of the "Rule 19" elementary cellular automaton starting with a single ON (black) cell. 4
 1, 5, 0, 127, 0, 2047, 0, 32767, 0, 524287, 0, 8388607, 0, 134217727, 0, 2147483647, 0, 34359738367, 0, 549755813887, 0, 8796093022207, 0, 140737488355327, 0, 2251799813685247, 0, 36028797018963967, 0, 576460752303423487, 0, 9223372036854775807, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55. LINKS Robert Price, Table of n, a(n) for n = 0..500 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton 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) = 17*a(n-2) - 16*a(n-4) for n>5. G.f.: (1+5*x-17*x^2+42*x^3+16*x^4-32*x^5) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)). (End) a(n) = (1-(-1)^n)*(4*16^floor(n/2)-1/2) for n>1. - Bruno Berselli, Dec 29 2015 a(n) = (2*4^n - 1)*(n mod 2) + 0^n - 2*0^abs(n-1). - Karl V. Keller, Jr., Sep 02 2021 E.g.f.: 1 - 2*x - sinh(x) + 2*sinh(4*x). - Stefano Spezia, Sep 03 2021 MATHEMATICA rule=19; 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 (MAGMA) [n le 1 select 5^n else (1-(-1)^n)*(4*16^Floor(n/2)-1/2): n in [0..40]]; // Bruno Berselli, Dec 29 2015 (Python) print([(2*4**n - 1)*(n%2) + 0**n - 2*0**abs(n-1) for n in range(50)]) # Karl V. Keller, Jr., Sep 02 2021 CROSSREFS Cf. A266155, A266323. Sequence in context: A122045 A294314 A347599 * A073911 A157302 A275759 Adjacent sequences:  A266321 A266322 A266323 * A266325 A266326 A266327 KEYWORD nonn,easy AUTHOR Robert Price, Dec 27 2015 STATUS approved

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Last modified November 30 20:17 EST 2021. Contains 349425 sequences. (Running on oeis4.)