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A027559
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Number of 4-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=4.
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1
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1, 2, 4, 8, 16, 30, 58, 106, 200, 360, 668, 1190, 2182, 3858, 7012, 12328, 22256, 38958, 69962, 122042, 218248, 379656, 676636, 1174390, 2087222, 3615906, 6411716, 11090504, 19627984, 33907134, 59912410, 103385482, 182429768
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a_n = a_{n-1} + 4a_{n-2} - 3a_{n-3} - 3a_{n-4}.
a_0 = 1; for n>0 odd, a_n = 7 * 3^floor{n/2} - F_{n+4}; for n>0 even, a_n = 4 * 3^floor{n/2} - F_{n+4} where F_n is the n-th Fibonacci number. - Barry Guiduli (guiduli(AT)gmail.com), Jun 23 2005
G.f. (1+x-2x^2-x^3+x^4) / ((1-x-x^2)(1-3x^2)). - David Callan (callan(AT)stat.wisc.edu), Jul 22 2008
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CROSSREFS
| Sequence in context: A164185 A164180 A164179 * A135492 A164191 A164193
Adjacent sequences: A027556 A027557 A027558 * A027560 A027561 A027562
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KEYWORD
| nonn
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AUTHOR
| R. K. Guy (rkg(AT)cpsc.ucalgary.ca) and David Callan (callan(AT)bayes.stat.wisc.edu)
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