# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a038184 Showing 1-1 of 1 %I A038184 #48 Dec 16 2021 11:38:34 %S A038184 1,7,21,107,273,1911,5189,28123,65793,460551,1381653,7039851,17829905, %T A038184 124809335,340873541,1840690907,4295032833,30065229831,90195689493, %U A038184 459568513131,1172543963409,8207807743863,22286925370437 %N 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. %C A038184 Generation n (starting from the generation 0: 1) interpreted as a binary number, but written in base 10. %C A038184 Rows of the mod 2 trinomial triangle (A027907), interpreted as binary numbers: 1, 111, 10101, 1101011, ... (A118110). - _Jacob A. Siehler_, Aug 25 2006 %C A038184 See A071053 for number of ON cells. - _N. J. A. Sloane_, Jul 28 2014 %H A038184 Gheorghe Coserea, Table of n, a(n) for n = 0..200 %H A038184 Alan J. Macfarlane, On generating functions of some sequences of integers defined in the evolution of the cellular automaton Rule 150, Preprint 2016. %H A038184 Eric Weisstein's World of Mathematics, Rule 150 %H A038184 Index entries for sequences related to cellular automata %e A038184 Bit patterns with "0" replaced by "." for visibilty [_Georg Fischer_, Dec 16 2021]: %e A038184 0: 1 %e A038184 1: 111 %e A038184 2: 1.1.1 %e A038184 3: 11.1.11 %e A038184 4: 1...1...1 %e A038184 5: 111.111.111 %e A038184 6: 1.1...1...1.1 %e A038184 7: 11.11.111.11.11 %e A038184 8: 1.......1.......1 %e A038184 9: 111.....111.....111 %e A038184 10: 1.1.1...1.1.1...1.1.1 %e A038184 11: 11.1.11.11.1.11.11.1.11 %e A038184 12: 1...1.......1.......1...1 %e A038184 13: 111.111.....111.....111.111 %e A038184 14: 1.1...1.1...1.1.1...1.1...1.1 %e A038184 15: 11.11.11.11.11.1.11.11.11.11.11 %p A038184 bit_n := (x,n) -> `mod`(floor(x/(2^n)),2); %p A038184 sigmagen := proc(n) option remember: if (0 = n) then (1) %p A038184 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: %t A038184 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 *) %o A038184 (PARI) %o A038184 a(n) = subst(lift(Pol(Mod([1,1,1],2),'x)^n),'x,2); %o A038184 vector(23,n,a(n-1)) \\ _Gheorghe Coserea_, Jun 12 2016 %Y A038184 Cf. A006977, A006978, A038183, A038185 (other cellular automata). %Y A038184 Cf. A048710, A048720, A027907, A001317, A071053. %Y A038184 This sequence, A071036 and A118110 are equivalent descriptions of the Rule 150 automaton. %K A038184 nonn %O A038184 0,2 %A A038184 _Antti Karttunen_, Feb 15 1999 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE