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A034933
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Number of solutions to a^2+b^2+3*c^2=n.
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3
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1, 4, 4, 2, 12, 16, 0, 8, 20, 4, 8, 8, 10, 32, 8, 0, 28, 24, 4, 8, 32, 16, 16, 16, 0, 28, 8, 2, 40, 48, 8, 8, 52, 0, 8, 16, 12, 64, 16, 8, 40, 24, 0, 24, 40, 16, 16, 16, 26, 28, 20, 0, 64, 80, 0, 16, 40, 24, 24, 8, 0, 64, 24, 8, 60, 48, 8, 24, 72, 0, 16, 16, 20, 48, 24, 10, 40, 96
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| Expansion of theta_3(q)^2*theta_3(q^3).
Euler transform of period 12 sequence [4, -6, 6, -2, 4, -9, 4, -2, 6, -6, 4, -3, ...]. - Michael Somos Sep 21 2005
Expansion of (eta(q^2)^2*eta(q^6))^5/(eta(q)^2*eta(q^3)*eta(q^4)^2*eta(q^12))^2 in power of q. - Michael Somos Sep 21 2005
G.f.: theta_3(q)^2*theta_3(q^3).
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EXAMPLE
| 1 +4*q +4*q^2 +2*q^3 +12*q^4 +16*q^5 +8*q^7 +20*q^8 +4*q^9 +...
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PROG
| (PARI) a(n)=if(n<1, n==0, qfrep([1, 0, 0; 0, 1, 0; 0, 0, 3], n)[n]*2) /* Michael Somos Sep 21 2005 */
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CROSSREFS
| Sequence in context: A151966 A010778 A202322 * A188657 A021697 A016707
Adjacent sequences: A034930 A034931 A034932 * A034934 A034935 A034936
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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