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A103128
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a(n) = floor(sqrt(2n-1)).
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10
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1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12
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OFFSET
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1,3
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COMMENTS
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n appears 2 * ceiling(n/2) times.
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LINKS
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FORMULA
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a(n+1) = a(n)+1 for n in A007590, otherwise a(n+1) = a(n).
G.f.: x*Theta3(x^2)/(2*(1-x)) + sqrt(x)*Theta2(x^2)/(2*(1-x)) - x/(2*(1-x)), where Theta2 and Theta3 are Jacobi Theta functions. (End)
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MAPLE
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MATHEMATICA
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PROG
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(Haskell)
a103128 = a000196 . (subtract 1) . (* 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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EXTENSIONS
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STATUS
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approved
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