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A164402
Number of binary strings of length n with no substrings equal to 0010 or 0110.
1
1, 2, 4, 8, 14, 24, 40, 68, 116, 200, 344, 592, 1016, 1744, 2992, 5136, 8816, 15136, 25984, 44608, 76576, 131456, 225664, 387392, 665024, 1141632, 1959808, 3364352, 5775488, 9914624, 17020160, 29218048, 50157824, 86104576, 147813376, 253747200
OFFSET
0,2
FORMULA
a(n) = 2*a(n-1) - 2*a(n-3) + 2*a(n-4). - Andrew Howroyd, Feb 14 2018
G.f.: (1 + 2*x^3)/(1 - 2*x + 2*x^3 - 2*x^4). - R. J. Mathar, Nov 30 2011
MATHEMATICA
LinearRecurrence[{2, 0, -2, 2}, {1, 2, 4, 8}, 50] (* G. C. Greubel, Sep 19 2017 *)
PROG
(PARI) Vec((1 + 2*x^3)/(1 - 2*x + 2*x^3 - 2*x^4) + O(x^40)) \\ G. C. Greubel, Sep 19 2017
CROSSREFS
Sequence in context: A019274 A164173 A164162 * A164165 A164168 A182747
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 14 2009
EXTENSIONS
a(0)-a(3) prepended by Andrew Howroyd, Feb 14 2018
STATUS
approved