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 A181533 Number of values generated by the algorithm given as first comment. 0
 2, 4, 8, 8, 12, 34, 58, 96, 188, 334, 574, 1046, 1874, 3308, 5928, 10608, 18872, 33694, 60194, 107338, 191542, 341950, 610146, 1088790, 1943262, 3467858, 6188534, 11044356, 19709736, 35173564 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 1) Generate all 2^n different binary string of n bits. 2) For each string apply the following rules: 2.A) if the i-th bit of the string is 1: the i-th bit of the result is 1 if and only if the (i-1)-th (mod n) AND the (i+1)-th (mod n) bit of the string is 1 2.B) if the i-th bit of the string is 0: the i-th bit of the result is 1 if and only if the (i-1)-th (mod n) OR the (i+1)-th (mod n) bit of the string is 1 For example: If the original string is 10010, then the result of the algorithm is 01101. The sequence counts the different possible values generated by the algorithm for all binary strings of length n. LINKS EXAMPLE For n=4 the 8 possible results generated by the algorithm are: [1001, 0000, 0011, 1111, 0110, 0101, 1010, 1100]. PROG (PARI) padbin(i, n) = {b = binary(i); off = n - #b; vector(n, i, if (i> off, b[i - off], 0)); } kprec(k, n) = if (kp = k-1, kp, n); knext(k, n) = if ((kn = k+1) > n, 1, kn); binv(v) = subst(Pol(v), x, 2); transf(v, n) = {tv = vector(n); for (k=1, n, kp = kprec(k, n); kn = knext(k, n); if (v[k], if ((v[kp] == 1) && (v[kn] == 1), tv[k] = 1), if ((v[kp] == 1) || (v[kn] == 1), tv[k] = 1); ); ); tv; } a(n) = {alls = []; for (i=0, 2^n-1, alls = Set(concat(alls, binv(transf(padbin(i, n), n)))); ); #alls; } \\ Michel Marcus, Apr 21 2014 CROSSREFS Sequence in context: A008218 A073043 A083542 * A263981 A088244 A073616 Adjacent sequences:  A181530 A181531 A181532 * A181534 A181535 A181536 KEYWORD nonn,base AUTHOR Arthur Oviedo (aa.oviedo332(AT)uniandes.edu.co), Oct 28 2010 EXTENSIONS a(12)-a(20) from Michel Marcus, Apr 21 2014 a(21)-a(30) from Giovanni Resta, Apr 22 2014 STATUS approved

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Last modified October 14 09:25 EDT 2019. Contains 327995 sequences. (Running on oeis4.)