cp's OEIS Frontend

A245191 Successive states of one-sided one-dimensional cellular automaton using Rule 90, starting with a single ON cell, converted to decimal.

%I A245191 #22 Jun 30 2018 21:16:33
%S A245191 1,2,5,8,20,34,85,128,320,544,1360,2056,5140,8738,21845,32768,81920,
%T A245191 139264,348160,526336,1315840,2236928,5592320,8388736,20971840,
%U A245191 35652128,89130320,134744072,336860180,572662306,1431655765,2147483648,5368709120,9126805504
%N A245191 Successive states of one-sided one-dimensional cellular automaton using Rule 90, starting with a single ON cell, converted to decimal.
%C A245191 The cells are labeled 0,1,2,3,4,5,6,... and we start at time 0 with cell 0 equal to 1, the rest 0.
%C A245191 At each step, the state of a cell is the mod 2 sum of the states of its left and right neighbors at the previous step (subject to the constraint that we only consider cells with nonnegative labels).
%C A245191 a(n) gives the state of the system, read from right to left, converted from binary to decimal.
%C A245191 This is a one-sided version of A038183.
%H A245191 Lars Blomberg, <a href="/A245191/b245191.txt">Table of n, a(n) for n = 0..100</a>
%F A245191 a(n) = Sum_{i>=0, i==n mod 2} (binomial(2n+2,n+2+i) mod 2)*2^i.
%F A245191 Write n = 2^k-1+j (k>=0, 0<=j<2^k). Then a(n) = 2^(k-j+1)*A038183(j).
%e A245191 Successive states are:
%e A245191 1
%e A245191 01
%e A245191 101
%e A245191 0001
%e A245191 00101
%e A245191 010001
%e A245191 1010101
%e A245191 00000001
%e A245191 000000101
%e A245191 0000010001
%e A245191 ...
%e A245191 which when converted from binary to decimal give the sequence.
%e A245191 This is the right-hand portion of the triangle in A038183.
%t A245191 a[ n_] := Sum[ Mod[Binomial[2 n + 2, n + i + 2], 2] 2^i, {i, Mod[n, 2], n}]; (* _Michael Somos_, Jun 30 2018 *)
%o A245191 (C)
%o A245191 #include <stdio.h>
%o A245191 int main()
%o A245191 {
%o A245191         int u = 1, i = 1, n = 20;
%o A245191         while (i++ <= n)
%o A245191         {
%o A245191                 printf("%d, ", u);
%o A245191                 u = (u >> 1) ^ (u << 1);
%o A245191         }
%o A245191 } /* _Luc Rousseau_, Jun 05 2018 */
%Y A245191 Cf. A038183, A189007.
%K A245191 nonn
%O A245191 0,2
%A A245191 _N. J. A. Sloane_, Jul 21 2014
%E A245191 Corrected a(11) and more terms from _Lars Blomberg_, Aug 08 2015