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 A266442 Binary representation of the n-th iteration of the "Rule 25" elementary cellular automaton starting with a single ON (black) cell. 2
 1, 1, 1010, 1000011, 1110100, 11010000111, 11101000, 111110100001111, 111010000, 1111111101000011111, 1110100000, 11111111111010000111111, 11101000000, 111111111111110100001111111, 111010000000, 1111111111111111101000011111111, 1110100000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Robert Price, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55. Index entries for sequences related to cellular automata Index to Elementary Cellular Automata Index entries for linear recurrences with constant coefficients, signature (0,10011,0,-110010,0,100000). FORMULA From Colin Barker, Jan 01 2016 and Apr 16 2019: (Start) a(n) = 10011*a(n-2) - 110010*a(n-4) + 100000*a(n-6) for n>9. G.f.: (1 +x -9001*x^2 +990000*x^3 -8891000*x^4 +999000000*x^5 -10991100000*x^6 +999000000000*x^7 +11000000000*x^8 -1000000000000*x^9) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)*(1 -10*x^2)). (End) a(n) = (10*100^n - 909999*10^((n+1)/2) - 1)/9 for odd n>3; a(n) = 11101*10^(n/2) for even n>2. - Karl V. Keller, Jr., Sep 02 2021 MATHEMATICA rule=25; 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]]], {k, 1, rows}] (* Binary Representation of Rows *) PROG (Python) print([1, 1, 10, 1000011] + [(10*100**n - 909999*10**((n+1)//2) - 1)//9 if n%2 else 11101*10**(n//2) for n in range(4, 50)]) # Karl V. Keller, Jr., Sep 02 2021 CROSSREFS Cf. A266441, A266443. Sequence in context: A157010 A076940 A173521 * A266673 A055473 A317526 Adjacent sequences: A266439 A266440 A266441 * A266443 A266444 A266445 KEYWORD nonn,easy AUTHOR Robert Price, Dec 29 2015 STATUS approved

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Last modified December 1 15:58 EST 2023. Contains 367485 sequences. (Running on oeis4.)