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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 15 1999
STATUS
approved