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A089800
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Expansion of Jacobi theta function theta_2(q)/q^(1/4).
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2
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2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0,1
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LINKS
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FORMULA
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For n > 0, a(n) = 2*(floor(sqrt(n+1/4)-1/2) - floor(sqrt(n-1+1/4)-1/2)). - Mikael Aaltonen, Jan 18 2015
a(n) = 2*(floor(sqrt(n+1)+1/2)-floor(sqrt(n)+1/2)). - Mikael Aaltonen, Jan 20 2015
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MAPLE
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if issqr(1+4*n) then
if type( sqrt(1+4*n)-1, 'even') then
2;
else
0;
end if;
else
0;
end if;
end proc:
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MATHEMATICA
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a[n_] := SeriesCoefficient[ EllipticTheta[2, 0, q]/q^(1/4), {q, 0, n}]; Table[a[n], {n, 0, 101}] (* Jean-François Alcover, Nov 12 2012 *)
Table[2*(Floor[Sqrt[n+1]+1/2] - Floor[Sqrt[n]+1/2]), {n, 0, 50}] (* G. C. Greubel, Nov 20 2017 *)
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PROG
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(PARI) for(n=0, 50, print1(2*(floor(sqrt(n+1)+1/2) - floor(sqrt(n)+1/2)), ", ")) \\ G. C. Greubel, Nov 20 2017
(Magma) [2*(Floor(Sqrt(n+1)+1/2) - Floor(Sqrt(n)+1/2)): n in [0..50]]; // G. C. Greubel, Nov 20 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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