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 A245191 Successive states of one-sided one-dimensional cellular automaton using Rule 90, starting with a single ON cell, converted to decimal. 3
 1, 2, 5, 8, 20, 34, 85, 128, 320, 544, 1360, 2056, 5140, 8738, 21845, 32768, 81920, 139264, 348160, 526336, 1315840, 2236928, 5592320, 8388736, 20971840, 35652128, 89130320, 134744072, 336860180, 572662306, 1431655765, 2147483648, 5368709120, 9126805504 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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. 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). a(n) gives the state of the system, read from right to left, converted from binary to decimal. This is a one-sided version of A038183. LINKS Lars Blomberg, Table of n, a(n) for n = 0..100 FORMULA a(n) = Sum_{i>=0, i==n mod 2} (binomial(2n+2,n+2+i) mod 2)*2^i. Write n = 2^k-1+j (k>=0, 0<=j<2^k). Then a(n) = 2^(k-j+1)*A038183(j). EXAMPLE Successive states are: 1 01 101 0001 00101 010001 1010101 00000001 000000101 0000010001 ... which when converted from binary to decimal give the sequence. This is the right-hand portion of the triangle in A038183. MATHEMATICA a[ n_] := Sum[ Mod[Binomial[2 n + 2, n + i + 2], 2] 2^i, {i, Mod[n, 2], n}]; (* Michael Somos, Jun 30 2018 *) PROG (C) #include int main() {         int u = 1, i = 1, n = 20;         while (i++ <= n)         {                 printf("%d, ", u);                 u = (u >> 1) ^ (u << 1);         } } /* Luc Rousseau, Jun 05 2018 */ CROSSREFS Cf. A038183, A189007. Sequence in context: A127281 A054774 A104721 * A281104 A139407 A107384 Adjacent sequences:  A245188 A245189 A245190 * A245192 A245193 A245194 KEYWORD nonn AUTHOR N. J. A. Sloane, Jul 21 2014 EXTENSIONS Corrected a(11) and more terms from Lars Blomberg, Aug 08 2015 STATUS approved

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Last modified October 14 08:54 EDT 2019. Contains 327995 sequences. (Running on oeis4.)