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A164393
Number of binary strings of length n with no substrings equal to 0001 or 0011.
1
1, 2, 4, 8, 14, 25, 44, 76, 132, 228, 393, 678, 1168, 2012, 3466, 5969, 10280, 17704, 30488, 52504, 90417, 155706, 268140, 461760, 795190, 1369385, 2358196, 4061012, 6993404, 12043228, 20739449, 35715070, 61504344, 105915636, 182395602, 314100513
OFFSET
0,2
FORMULA
a(n) = 2*a(n-1) - 2*a(n-4) + a(n-5). - Andrew Howroyd, Feb 14 2018
G.f.: 1/((1 - x)*(1 - x - x^2 - x^3 + x^4)). - R. J. Mathar, Dec 01 2011
MATHEMATICA
LinearRecurrence[{2, 0, 0, -2, 1}, {1, 2, 4, 8, 14}, 50] (* G. C. Greubel, Sep 18 2017 *)
PROG
(PARI) Vec(1/((1 - x)*(1 - x - x^2 - x^3 + x^4)) + O(x^40)) \\ G. C. Greubel, Sep 18 2017
CROSSREFS
Sequence in context: A291443 A210145 A020956 * A164391 A164153 A212588
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 14 2009
EXTENSIONS
a(0)-a(3) prepended by Andrew Howroyd, Feb 14 2018
STATUS
approved