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A102315
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Expansion of (b(q^6)*c(q^6))/(b(q^3)*c(q^3)) in powers of q where b(),c() are cubic AGM analog functions.
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0
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1, 2, 3, 8, 13, 20, 37, 56, 83, 134, 196, 280, 419, 592, 824, 1176, 1618, 2202, 3040, 4096, 5471, 7368, 9753, 12824, 16937, 22090, 28653, 37248, 47968, 61488, 78887, 100472, 127461, 161702, 203951, 256368, 322090, 402748, 502112, 625464, 776061
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| Euler transform of period 6 sequence [2, 0, 4, 0, 2, 0, ...].
Given g.f. A(x), then B(x)=A(x^3)x satisfies 0=f(B(x), B(x^2)) where f(u, v)=u^2-v-4uv^2.
Expansion of q^(-1)(eta(q^2)*eta(q^6)/(eta(q)*eta(q^3)))^2 in powers of q^3.
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EXAMPLE
| q +2*q^4 +3*q^7 +8*q^10 +13*q^13 +20*q^16 +37*q^19 +56*q^22 +...
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PROG
| (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (eta(x^2+A)*eta(x^6+A)/eta(x+A)/eta(x^3+A))^2, n))}
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CROSSREFS
| Sequence in context: A168343 A080478 A002053 * A142880 A147329 A175148
Adjacent sequences: A102312 A102313 A102314 * A102316 A102317 A102318
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Jan 04 2005
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