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 A027557 Number of 3-balanced strings of length n: let d(S)= #(1)'s in S - #(0)'s, then S is k-balanced if every substring T has -k<=d(T)<=k; here k=3. 1
 1, 2, 4, 8, 14, 26, 44, 78, 130, 224, 370, 626, 1028, 1718, 2810, 4656, 7594, 12506, 20356, 33374, 54242, 88640, 143906, 234594, 380548, 619238, 1003882, 1631312, 2643386, 4291082, 6950852, 11274702, 18258322, 29598560 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA a_n = a_{n-1} + 3a_{n-2} - 2a_{n-3} - 2a_{n-4}; g.f. (1+x-x^2) / (1-x-x^2)(1-2x^2). a(n) = 2*A000045(n+3) - 2^floor((n+2)/2) - 2^floor((n+1)/2) - Max Alekseyev, Jun 02 2005 MATHEMATICA LinearRecurrence[{1, 3, -2, -2}, {1, 2, 4, 8}, 40] (* From Harvey P. Dale, Feb 01 2012 *) PROG (PARI) a(n) = 2*fibonacci(n+3) - 2^((n+2)\2) - 2^((n+1)\2) (Alekseyev) CROSSREFS Sequence in context: A208483 A006777 A036609 * A120545 A130708 A054193 Adjacent sequences:  A027554 A027555 A027556 * A027558 A027559 A027560 KEYWORD nonn AUTHOR R. K. Guy, callan(AT)bayes.stat.wisc.edu (David Callan) STATUS approved

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