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.

1, 7, 21, 107, 273, 1911, 5189, 28123, 65793, 460551, 1381653, 7039851, 17829905, 124809335, 340873541, 1840690907, 4295032833, 30065229831, 90195689493, 459568513131, 1172543963409, 8207807743863, 22286925370437

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

Alan J. Macfarlane, On generating functions of some sequences of integers defined in the evolution of the cellular automaton Rule 150, Preprint 2016.

Eric Weisstein's World of Mathematics, Rule 150

Index entries for sequences related to cellular automata

Example

Bit patterns with "0" replaced by "." for visibilty [Georg Fischer, Dec 16 2021]:
  0:                    1
  1:                   111
  2:                  1.1.1
  3:                 11.1.11
  4:                1...1...1
  5:               111.111.111
  6:              1.1...1...1.1
  7:             11.11.111.11.11
  8:            1.......1.......1
  9:           111.....111.....111
  10:         1.1.1...1.1.1...1.1.1
  11:        11.1.11.11.1.11.11.1.11
  12:       1...1.......1.......1...1
  13:      111.111.....111.....111.111
  14:     1.1...1.1...1.1.1...1.1...1.1
  15:    11.11.11.11.11.1.11.11.11.11.11

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