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Search: id:A033712
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| A033712 |
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theta3(z)*theta3(2z)*theta3(3z)*theta3(6z). |
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+0
1
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| 1, 2, 2, 6, 6, 4, 14, 8, 6, 26, 12, 16, 42, 12, 16, 44, 6, 20, 50, 16, 36, 56, 24, 16, 42, 30, 28, 78, 48, 36, 84, 40, 6, 80, 36, 48, 150, 44, 40, 100, 36, 36, 112, 48, 72, 148, 48, 48, 42, 50, 62, 124, 84, 52, 158, 64, 48, 144, 60, 64, 252, 60, 64, 200, 6, 88, 168, 64, 108
(list; graph; listen)
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OFFSET
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0,2
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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. 102, eq. 9.
L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 3, p. 225.
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FORMULA
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Number of solutions to a^2+2*b^2+3*c^2+6*d^2=n in integers.
Expansion of (eta(q^2)eta(q^4)eta(q^6)eta(q^12))^3/(eta(q)eta(q^3)eta(q^8)eta(q^24))^2 in powers of q.
Euler transform of period 24 sequence [2, -1, 4, -4, 2, -2, 2, -2, 4, -1, 2, -8, 2, -1, 4, -2, 2, -2, 2, -4, 4, -1, 2, -4, ...]. - Michael Somos, May 30 2005
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EXAMPLE
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1+2*q+2*q^2+6*q^3+6*q^4+4*q^5+14*q^6+8*q^7+...
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, A=sum(k=1, sqrtint(n), 2*x^k^2, 1+x*O(x^n)); polcoeff( A* subst(A+x*O(x^(n\2)), x, x^2)* subst(A+x*O(x^(n\3)), x, x^3)* subst(A+x*O(x^(n\6)), x, x^6), n))} /* Michael Somos May 30 2005 */
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CROSSREFS
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Sequence in context: A056881 A060779 A029594 this_sequence A033730 A033754 A063944
Adjacent sequences: A033709 A033710 A033711 this_sequence A033713 A033714 A033715
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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