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A033683 a(n) = 1 if n is an odd square not divisible by 3, otherwise 0. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
REFERENCES
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 105, Eq. (41).
LINKS
FORMULA
Essentially the series psi_6(z)=(1/2)(theta_2(z/9)-theta_2(z)).
a(A104777(n)) = 1.
A080995(n) = a(24n+1).
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
a(n) = A033684(n) * A000035(n).
Dirichlet g.f.: zeta(2*s) *(1-2^(-2s)) *(1-3^(-2s)). - R. J. Mathar, Mar 10 2011
G.f.: Sum_{k in Z} x^(6*k+1)^2. - Michael Somos, Dec 07 2019
Sum_{k=1..n} a(k) ~ sqrt(n)/3. - Amiram Eldar, Jan 14 2024
EXAMPLE
G.f. = x + x^25 + x^49 + x^121 + x^169 + x^289 + x^361 + x^529 + x^625 + ...
MATHEMATICA
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 *)
PROG
(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
-- Reinhard Zumkeller, Nov 14 2015
(Magma) Basis( ModularForms( Gamma0(144), 1/2), 106)[2]; /* Michael Somos, Dec 07 2019 */
CROSSREFS
Sequence in context: A178333 A063524 A326168 * A216284 A360109 A355452
KEYWORD
nonn,mult,easy
AUTHOR
STATUS
approved

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Last modified March 18 22:34 EDT 2024. Contains 370951 sequences. (Running on oeis4.)