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A117077
Define binary strings S(0)=0, S(1)=1, S(n) = S(n-2)S(n-1); a(n) = S(n) converted to decimal.
0
0, 1, 1, 5, 13, 173, 3501, 1420717, 7343549869, 24407739551034797, 264579267653248177273154989, 15107659029337673520218077770654501397966253, 5900314832748922900613950065282124787723453785544193308390237364661677
OFFSET
0,4
COMMENTS
Note that S(n) in general has leading zeros.
FORMULA
S(0) = 0, S(1) = 1, so S(2) = 01, a(2) = 1.
Use the substitution system 0->1 and 1->01. The values generated from a(0)=0 are 1, 01, 101, 01101, which in base 10 give the sequence. - Jon Perry, Feb 06 2011
EXAMPLE
S(3) = 01 (base 2) = 1 (base 10) so a(3) = 1.
S(4) = 101 (base 2) = 5 (base 10) so a(4) = 5.
S(5) = 01.101 = 01101 (base 2) = 13 (base 10) so a(5) = 13.
S(6) = 101.01101 = 10101101 (base 2) = 173 (base 10) so a(6) = 173.
S(7) = 01101.10101101 = 0110110101101 (base 2) = 3501 (base 10).
MATHEMATICA
a[1] = 0; a[2] = 1; a[n_] := a[n] = If[ OddQ@n, FromDigits[ Join[ IntegerDigits[ a[n - 2], 2], IntegerDigits[ a[n - 1], 2]], 2], FromDigits[ Join[ IntegerDigits[ a[n - 2], 2], {0}, IntegerDigits[ a[n - 1], 2]], 2]]; Array[a, 13] (* Robert G. Wilson v, Apr 20 2006 *)
CROSSREFS
Cf. A063896.
Sequence in context: A187894 A214591 A159261 * A124924 A209271 A352083
KEYWORD
base,nonn
AUTHOR
Jordan Goldstein (jboymicro20X6(AT)aim.com), Apr 18 2006
EXTENSIONS
More terms from Robert G. Wilson v, Apr 20 2006
Edited by N. J. A. Sloane, Apr 23 2006
STATUS
approved