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Search: id:A034896
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| A034896 |
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Number of solutions to a^2+b^2+3*c^2+3*d^2=n. |
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3
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| 1, 4, 4, 4, 20, 24, 4, 32, 52, 4, 24, 48, 20, 56, 32, 24, 116, 72, 4, 80, 120, 32, 48, 96, 52, 124, 56, 4, 160, 120, 24, 128, 244, 48, 72, 192, 20, 152, 80, 56, 312, 168, 32, 176, 240, 24, 96, 192, 116, 228, 124, 72, 280, 216, 4, 288, 416, 80, 120, 240, 120, 248, 128, 32, 500
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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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. 229.
N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 79, Eq. (32.3), p. 76, Eq. (31.43).
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LINKS
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Michael Gilleland, Some Self-Similar Integer Sequences
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FORMULA
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Expansion of theta_3(q)^2*theta_3(q^3)^2.
G.f.: s(2)^10*s(6)^10/(s(1)*s(3)*s(4)*s(12))^4, where s(k) := subs(q=q^k, eta(q)) and eta(q) is Dedekind's function, cf. A010815. [Fine]
Fine gives an explicit formula for a(n) in terms of the divisors of n.
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CROSSREFS
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Sequence in context: A141666 A102127 A131946 this_sequence A120914 A024949 A059812
Adjacent sequences: A034893 A034894 A034895 this_sequence A034897 A034898 A034899
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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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