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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. 12
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

LINKS

Gheorghe Coserea, Table of n, a(n) for n = 0..200

Eric Weisstein's World of Mathematics, Rule 150

Index entries for sequences related to cellular automata

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 A061961

Adjacent sequences:  A038181 A038182 A038183 * A038185 A038186 A038187

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 15 1999

STATUS

approved

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Last modified August 27 09:12 EDT 2016. Contains 275904 sequences.