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A033717
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Number of integer solutions to the equation x^2+2y^2+4z^2=n.
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1
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1, 2, 2, 4, 4, 4, 8, 8, 6, 6, 8, 4, 8, 12, 0, 8, 12, 8, 10, 12, 8, 8, 24, 8, 8, 14, 8, 16, 16, 4, 0, 16, 6, 16, 16, 8, 12, 20, 24, 8, 24, 8, 16, 20, 8, 20, 0, 16, 24, 18, 10, 8, 24, 12, 32, 24, 0, 16, 24, 12, 16, 20, 0, 24, 12, 8, 16, 28, 16, 16, 48, 8, 30, 32, 8, 20, 24, 16, 0, 16, 24, 18
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Euler transform of period 16 sequence [2,-1,2,-2,2,-1,2,-5,2,-1,2,-2,2,-1,2,-3,...].
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REFERENCES
| J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p 102 eq 9.
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FORMULA
| G.f.: theta3(q)theta3(q^2)theta3(q^4).
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PROG
| (PARI) a(n)=local(X); if(n<0, 0, X=x+x*O(x^n); polcoeff(eta(X)^-2*eta(X^2)^3*eta(X^4)*eta(X^8)^3*eta(X^16)^-2, n))
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CROSSREFS
| Sequence in context: A108514 A120456 A115383 * A033756 A124340 A071165
Adjacent sequences: A033714 A033715 A033716 * A033718 A033719 A033720
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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