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Search: id:A121652
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| A121652 |
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a(n) is the cube of the coefficient of x^n in 1/(1 - x*A(x^3)), where g.f. A(x) = Sum_{n>=0} a(n)*x^n. |
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+0
5
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| 1, 1, 1, 1, 8, 27, 64, 216, 729, 2197, 6859, 21952, 68921, 300763, 1061208, 3375000, 14348907, 54010152, 183250432, 716917375, 2685619000, 9460870875, 38136631896, 142973623989, 507024206424, 2042099126703, 7744763561625
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OFFSET
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0,5
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FORMULA
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a(n) = A121653(n)^3. G.f.: A(x^3) = (1 - 1/B(x) )/x, where B(x) = Sum_{n>=0} a(n)^(1/3)*x^n is the g.f. of A121653.
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EXAMPLE
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A(x) = 1 + x + x^2 + x^3 + 8*x^4 + 27*x^5 + 64*x^6 + 216*x^7 +...
Take the cube-root of each term, a(n)^(1/3) and
let B(x) be the g.f. of the resulting sequence:
B(x) = 1 + x + x^2 + x^3 + 2*x^4 + 3*x^5 + 4*x^6 + 6*x^7 + 9*x^8 +...
Then 1/B(x) = 1 - x*A(x^3):
1/B(x) = 1 - x - x^4 - x^7 - x^10 - 8*x^13 - 27*x^16 - 64*x^19 -...
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PROGRAM
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(PARI) {a(n)=if(n==0, 1, sum(k=0, n\3, polcoeff(x^(n-3*k)*(sum(j=0, k, a(j)*x^(3*j))+x*O(x^n))^(n-3*k), n))^3)}
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CROSSREFS
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Cf. A121653; trisections of A121653: A121654, A121655, A121656; variant: A121648.
Sequence in context: A076969 A050462 A112662 this_sequence A112989 A018832 A030293
Adjacent sequences: A121649 A121650 A121651 this_sequence A121653 A121654 A121655
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Aug 14 2006
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