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1, 1, 3, 1, 5, 3, 11, 5, 21, 11, 43, 21, 85, 43, 171, 85, 341, 171, 683, 341, 1365, 683, 2731, 1365, 5461, 2731, 10923, 5461, 21845, 10923, 43691, 21845, 87381, 43691, 174763, 87381, 349525, 174763, 699051, 349525, 1398101, 699051, 2796203, 1398101, 5592405
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OFFSET
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0,3
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COMMENTS
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Consider the Harmonacci sequence: H(1)=x, H(2)=y, H(3)=2xy/(x+y), H(4)=4xy/(3x+y)...; H(m) is the harmonic mean of H(m-1) and H(m-2). a(2n) and a(2n+1) are the denominator coefficients of H(n+3).
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LINKS
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FORMULA
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a(n) = (a(n-1)+1)/2 for n=2, 6, 10...
a(n) = 4*a(n-1)-1 for n=3, 7, 11...
a(n) = (a(n-1)-1)/2 for n=4, 8, 12...
a(n) = 4*a(n-1)+1 for n=5, 9, 13....
G.f.: (1 + x + 2*x^2) / ((1 + x^2)*(1 - 2*x^2)).
a(n) = a(n-2) + 2*a(n-4) for n>3.
(End)
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MATHEMATICA
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LinearRecurrence[{0, 1, 0, 2}, {1, 1, 3, 1}, 50] (* Harvey P. Dale, May 30 2018 *)
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PROG
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(PARI) Vec((1 + x + 2*x^2) / ((1 + x^2)*(1 - 2*x^2)) + O(x^60)) \\ Colin Barker, Dec 15 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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