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 A267255 Decimal representation of the n-th iteration of the "Rule 111" elementary cellular automaton starting with a single ON (black) cell. 1
 1, 6, 7, 122, 31, 2018, 95, 32738, 95, 524258, 95, 8388578, 95, 134217698, 95, 2147483618, 95, 34359738338, 95, 549755813858, 95, 8796093022178, 95, 140737488355298, 95, 2251799813685218, 95, 36028797018963938, 95, 576460752303423458, 95, 9223372036854775778 (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..1000 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton S. Wolfram, A New Kind of Science Index entries for linear recurrences with constant coefficients, signature (0,17,0,-16). FORMULA From Colin Barker, Jan 13 2016: (Start) a(n) = 17*a(n-2)-16*a(n-4) for n>8. G.f.: (1+6*x-10*x^2+20*x^3-72*x^4+40*x^5-320*x^6+384*x^7-1024*x^8) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)). (End) MATHEMATICA rule=111; 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+6*x-10*x^2+20*x^3-72*x^4+40*x^5-320*x^6+384*x^7-1024*x^8)/((1-x)*(1+x)*(1-4*x)*(1+4*x)) + O(x^30)) \\ Colin Barker, Jan 13 2016 CROSSREFS Cf. A267253. Sequence in context: A041081 A041082 A036417 * A041357 A041829 A042497 Adjacent sequences:  A267252 A267253 A267254 * A267256 A267257 A267258 KEYWORD nonn,easy AUTHOR Robert Price, Jan 12 2016 STATUS approved

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