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A033683
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a(n) = 1 if n is an odd square not divisible by 3, otherwise 0.
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6
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0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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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REFERENCES
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J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 105, Eq. (41).
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LINKS
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FORMULA
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Essentially the series psi_6(z)=(1/2)(theta_2(z/9)-theta_2(z)).
Multiplicative with a(p^e) = 1 if 2 divides e and p > 3, 0 otherwise. - Mitch Harris, Jun 09 2005
Euler transform of a period 144 sequence. - Michael Somos, Jan 26 2008
Dirichlet g.f.: zeta(2*s) *(1-2^(-2s)) *(1-3^(-2s)). - R. J. Mathar, Mar 10 2011
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EXAMPLE
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G.f. = x + x^25 + x^49 + x^121 + x^169 + x^289 + x^361 + x^529 + x^625 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ (EllipticTheta[ 2, 0, x^4] - EllipticTheta[ 2, 0, x^36])/2, {x, 0, n}] // PowerExpand; (* Michael Somos, Dec 07 2019 *)
Table[If[OddQ[n]&&IntegerQ[Sqrt[n]]&&Mod[n, 3]!=0, 1, 0], {n, 0, 120}] (* Harvey P. Dale, Sep 06 2020 *)
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PROG
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(PARI) {a(n) = if( n%24 == 1, issquare(n), 0)}; /* Michael Somos, Jan 26 2008 */
(Haskell)
a033683 n = fromEnum $ odd n && mod n 3 > 0 && a010052 n == 1
(Magma) Basis( ModularForms( Gamma0(144), 1/2), 106)[2]; /* Michael Somos, Dec 07 2019 */
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CROSSREFS
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KEYWORD
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nonn,mult,easy
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AUTHOR
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STATUS
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approved
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