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A059512
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For n>=2, the number of (s(0), s(1), ..., s(n-1)) such that 0 < s(i) < 5 and |s(i) - s(i-1)| <= 1 for i = 1,2,....,n-1, s(0) = 2, s(n-1) = 2.
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4
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0, 1, 1, 3, 7, 18, 46, 119, 309, 805, 2101, 5490, 14356, 37557, 98281, 257231, 673323, 1762594, 4614226, 12079707, 31624285, 82792161, 216750601, 567457058, 1485616392, 3889385353, 10182528721, 26658183099, 69791991919
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OFFSET
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0,4
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COMMENTS
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Substituting x(1-x)/(1-2x) into x/(1-x^2) yields g.f. of sequence.
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LINKS
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FORMULA
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a(n) = 2a(n-1) + Sum{m<n-1}a(m) - F(n-3) where F(n) is the n-th Fibonacci number (A000045).
G.f.: x(1-x)(1-2x)/((1-x-x^2)(1-3x+x^2)).
a(n+1)=sum{k=0..floor(n/2), C(n,2k)*F(2k+1)}. [From Paul Barry, Oct 14 2009]
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MATHEMATICA
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CoefficientList[Series[x(1-x)(1-2x)/((1-x-x^2)(1-3x+x^2)), {x, 0, 30}], x] (* Harvey P. Dale, Apr 23 2011 *)
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PROG
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(PARI) a(n)=(fibonacci(2*n-1)+fibonacci(n-2))/2
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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