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A027557
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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.
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1
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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
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..33.
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FORMULA
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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
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MATHEMATICA
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LinearRecurrence[{1, 3, -2, -2}, {1, 2, 4, 8}, 40] (* From Harvey P. Dale, Feb 01 2012 *)
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PROG
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(PARI) a(n) = 2*fibonacci(n+3) - 2^((n+2)\2) - 2^((n+1)\2) (Alekseyev)
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CROSSREFS
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Sequence in context: A208483 A006777 A036609 * A120545 A130708 A054193
Adjacent sequences: A027554 A027555 A027556 * A027558 A027559 A027560
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KEYWORD
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nonn
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AUTHOR
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R. K. Guy, callan(AT)bayes.stat.wisc.edu (David Callan)
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STATUS
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approved
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