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A082392
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Expansion of (1/x) * Sum_{k>=0} x^2^k / (1 - 2*x^2^(k+1)).
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5
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1, 1, 2, 1, 4, 2, 8, 1, 16, 4, 32, 2, 64, 8, 128, 1, 256, 16, 512, 4, 1024, 32, 2048, 2, 4096, 64, 8192, 8, 16384, 128, 32768, 1, 65536, 256, 131072, 16, 262144, 512, 524288, 4, 1048576, 1024, 2097152, 32, 4194304, 2048, 8388608, 2, 16777216
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OFFSET
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0,3
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LINKS
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FORMULA
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a(0) = 1, a(2*n) = 2^n, a(2*n+1) = a(n).
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MAPLE
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nmax := 48: for p from 0 to ceil(simplify(log[2](nmax))) do for n from 0 to ceil(nmax/(p+2))+1 do a((2*n+1)*2^p-1) := 2^n od: od: seq(a(n), n=0..nmax); # Johannes W. Meijer, Feb 11 2013
end proc:
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MATHEMATICA
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a[n_] := 2^(((n+1)/2^IntegerExponent[n+1, 2]+1)/2-1);
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PROG
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(PARI) for(n=0, 50, l=ceil(log(n+1)/log(2)); t=polcoeff(sum(k=0, l, (x^2^k)/(1-2*x^2^(k+1)))/x + O(x^(n+1)), n); print1(t", "); ) ;
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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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STATUS
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approved
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