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