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A001445
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a(n) = (2^n + 2^[ n/2 ] )/2.
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6
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3, 5, 10, 18, 36, 68, 136, 264, 528, 1040, 2080, 4128, 8256, 16448, 32896, 65664, 131328, 262400, 524800, 1049088, 2098176, 4195328, 8390656, 16779264, 33558528, 67112960, 134225920, 268443648
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OFFSET
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2,1
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COMMENTS
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LINKS
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FORMULA
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G.f.: x^2*(3-x-6*x^2)/((1-2*x)*(1-2*x^2)).
a(n) = 2*a(n-1) + 2*a(n-2) - 4*a(n-3) for n > 4. - Chai Wah Wu, Sep 10 2020
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EXAMPLE
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G.f. = 3*x^2 + 5*x^3 + 10*x^4 + 18*x^5 + 36*x^6 + 68*x^7 + 136*x^8 + ...
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MAPLE
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f := n->(2^n+2^floor(n/2))/2;
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MATHEMATICA
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Table[(2^n + 2^(Floor[n/2]))/2, {n, 2, 50}] (* G. C. Greubel, Sep 08 2017 *)
LinearRecurrence[{2, 2, -4}, {3, 5, 10}, 30] (* Harvey P. Dale, Sep 12 2021 *)
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PROG
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(PARI) for(n=2, 50, print1((2^n + 2^(n\2))/2, ", ")) \\ G. C. Greubel, Sep 08 2017
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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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