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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. 1
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

S. 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: (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

(PARI) Vec((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)) + O(x^30)) \\ Colin Barker, Dec 29 2015

(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

CROSSREFS

Cf. A260552.

Sequence in context: A052603 A071556 A145508 * A061425 A160605 A224759

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 February 21 14:40 EST 2018. Contains 299414 sequences. (Running on oeis4.)