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A112280
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Coefficients, read modulo 9, of the cube of q-series (q;q)_oo.
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2
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1, 6, 0, 5, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The cube-root of g.f. A(x) is an integer series (A112281).
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FORMULA
| G.f.: A(x) = Sum_{n>=0} A112282(n) * x^(n*(n+1)/2) where A112282(n) = (-1)^n*(2*n+1) (mod 9).
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EXAMPLE
| A(x) = 1 + 6*x + 5*x^3 + 2*x^6 + 0*x^10 + 7*x^15 + 4*x^21 +... = (1 - 3*x + 5*x^3 - 7*x^6 + 9*x^10 - 11*x^15 +...) (mod 9).
A(x)^(1/3) = 1 + 2*x - 4*x^2 + 15*x^3 - 60*x^4 + 268*x^5 -+...
Notation: q-series (q;q)_oo = Product_{n>=1} (1-q^n) = 1 + Sum_{n>=1} (-1)^n*[q^(n*(3*n-1)/2) + q^(n*(3*n+1)/2)].
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PROG
| (PARI) {a(n)=polcoeff(sum(k=0, sqrtint(2*n+1), (((-1)^k*(2*k+1))%9)*x^(k*(k+1)/2)+x*O(x^n)), n)}
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CROSSREFS
| Cf. A112281 (A(x)^(1/3)), A112282 (nonzero terms), A111983 (variant).
Sequence in context: A197148 A196623 A113024 * A204850 A202394 A202954
Adjacent sequences: A112277 A112278 A112279 * A112281 A112282 A112283
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Sep 01 2005
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