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 A038184 State of one-dimensional cellular automaton 'sigma' (Rule 150): 000,001,010,011,100,101,110,111 -> 0,1,1,0,1,0,0,1 at generation n, converted to a decimal number. 13
 1, 7, 21, 107, 273, 1911, 5189, 28123, 65793, 460551, 1381653, 7039851, 17829905, 124809335, 340873541, 1840690907, 4295032833, 30065229831, 90195689493, 459568513131, 1172543963409, 8207807743863, 22286925370437 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Generation n (starting from the generation 0: 1) interpreted as a binary number, but written in base 10. Rows of the mod 2 trinomial triangle (A027907), interpreted as binary numbers: 1, 111, 10101, 1101011, ... (A118110) - Jacob A. Siehler, Aug 25 2006 See A071053 for number of ON cells. - N. J. A. Sloane, Jul 28 2014 REFERENCES Alan J. Macfarlane, On generating functions of some sequences of integers defined in the evolution of the cellular automaton Rule 150, Preprint 2016; http://www.damtp.cam.ac.uk/user/ajm/Papers2016/CellularAutomatonRule150.ps LINKS Gheorghe Coserea, Table of n, a(n) for n = 0..200 Eric Weisstein's World of Mathematics, Rule 150 MAPLE bit_n := (x, n) -> `mod`(floor(x/(2^n)), 2); sigmagen := proc(n) option remember: if (0 = n) then (1) else sum('((bit_n(sigmagen(n-1), i)+bit_n(sigmagen(n-1), i-1)+bit_n(sigmagen(n-1), i-2)) mod 2)*(2^i)', 'i'=0..(2*n)) fi: end: MATHEMATICA f[n_] := Sum[2^k*Coefficient[ #, x, k], {k, 0, 2n}] & @ Expand[(1 + x + x^2)^n, Modulus -> 2] (* Jacob A. Siehler, Aug 25 2006 *) PROG (PARI) a(n) = subst(lift(Pol(Mod([1, 1, 1], 2), 'x)^n), 'x, 2); vector(23, n, a(n-1))  \\ Gheorghe Coserea, Jun 12 2016 CROSSREFS Cf. A006977, A006978, A038183, A038185 (other cellular automata). Cf. A048710, A048720, A027907, A001317, A071053. This sequence, A071036 and A118110 are equivalent descriptions of the Rule 150 automaton. Sequence in context: A253072 A261854 A219152 * A001185 A001693 A321521 Adjacent sequences:  A038181 A038182 A038183 * A038185 A038186 A038187 KEYWORD nonn AUTHOR Antti Karttunen, Feb 15 1999 STATUS approved

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Last modified October 20 21:27 EDT 2019. Contains 328273 sequences. (Running on oeis4.)