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A101921
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a(2n) = a(n) + 2n - 1, a(2n+1) = 4n.
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12
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0, 1, 4, 4, 8, 9, 12, 11, 16, 17, 20, 20, 24, 25, 28, 26, 32, 33, 36, 36, 40, 41, 44, 43, 48, 49, 52, 52, 56, 57, 60, 57, 64, 65, 68, 68, 72, 73, 76, 75, 80, 81, 84, 84, 88, 89, 92, 90, 96, 97, 100, 100, 104, 105, 108, 107, 112, 113, 116, 116, 120, 121, 124, 120, 128
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OFFSET
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1,3
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COMMENTS
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Exponent of 2 in tangent numbers A000182.
Also, exponent of 2 in 4^(n-1)/n. [David Brink, Aug 08 2013]
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LINKS
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FORMULA
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G.f.: Sum_{k>=0} t^2*(1+4*t+t^2)/(1-t^2)^2 where t=x^2^k.
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EXAMPLE
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G.f. = x^2 + 4*x^3 + 4*x^4 + 8*x^5 + 9*x^6 + 12*x^7 + 11*x^8 + 16*x^9 + 17*x^10 + ...
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MATHEMATICA
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a[n_]:= If[n<1, 0, 2n -2 - IntegerExponent[n, 2]]; (* Michael Somos, Mar 02 2014 *)
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PROG
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(PARI) a(n)=valuation(4^(n-1)/n, 2); \\ Joerg Arndt, Aug 13 2013
(Sage) [2*n-2 -valuation(n, 2) for n in (1..100)] # G. C. Greubel, Nov 29 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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