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 A266090 Decimal representation of the n-th iteration of the "Rule 17" elementary cellular automaton starting with a single ON (black) cell. 3
 1, 1, 8, 79, 64, 1663, 512, 29695, 4096, 499711, 32768, 8191999, 262144, 132644863, 2097152, 2134900735, 16777216, 34259075071, 134217728, 548950507519, 1073741824, 8789650571263, 8589934592, 140685948747775, 68719476736, 2251387496824831, 549755813888 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55. LINKS G. C. Greubel, Table of n, a(n) for n = 0..500 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 (0,25,0,-152,0,128). FORMULA From Colin Barker, Dec 29 2015 and Apr 15 2019: (Start) a(n) = 25*a(n-2)-152*a(n-4)+128*a(n-6) for n>5. G.f.: (1-2*x)*(1+3*x-11*x^2+32*x^3+80*x^4) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-8*x^2)). (End) a(n) = 8^(n/2) + (1-(-1)^n)*(2*4^n-8^(n/2)-6*8^((n-1)/2)-1)/2. Therefore: for even n, a(n) = 8^(n/2); otherwise, a(n) = 2*4^n - 6*8^((n-1)/2) - 1. - Bruno Berselli, Dec 29 2015 MATHEMATICA rule=17; 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 (Sage) [8^(n/2)+(1-(-1)^n)*(2*4^n-8^(n/2)-6*8^((n-1)/2)-1)/2 for n in [0..30]] # Bruno Berselli, Dec 29 2015 (Magma) [IsEven(n) select 8^(n div 2) else 2*4^n-6*8^((n-1) div 2)-1: n in [0..30]]; // Bruno Berselli, Dec 29 2015 (Python) print([2*4**n - 6*8**((n-1)//2) - 1 if n%2 else 8**(n//2) for n in range(50)]) # Karl V. Keller, Jr., Aug 31 2021 CROSSREFS Cf. A260552, A260692. Sequence in context: A316203 A303507 A145508 * A366214 A061425 A160605 Adjacent sequences: A266087 A266088 A266089 * A266091 A266092 A266093 KEYWORD nonn,easy AUTHOR Robert Price, Dec 27 2015 STATUS approved

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Last modified November 28 08:03 EST 2023. Contains 367394 sequences. (Running on oeis4.)