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Search: id:A121653
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| A121653 |
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G.f.: A(x) = 1/(1 - x*B(x^3)), where B(x) = Sum_{n>=0} a(n)^3*x^n is the g.f. of A121652. |
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+0
5
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| 1, 1, 1, 1, 2, 3, 4, 6, 9, 13, 19, 28, 41, 67, 102, 150, 243, 378, 568, 895, 1390, 2115, 3366, 5229, 7974, 12687, 19785, 30307, 47893, 74761, 115063, 181457, 283143, 436831, 687963, 1073820, 1659809, 2608418, 4072442, 6306619, 9980210, 15617469
(list; graph; listen)
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OFFSET
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0,5
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FORMULA
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a(n) = A121652(n)^(1/3).
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EXAMPLE
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A(x) = 1 + x + x^2 + x^3 + 2*x^4 + 3*x^5 + 4*x^6 + 6*x^7 + 9*x^8 +...
The coefficients of 1 - 1/A(x) equal the cube of each term:
1/A(x) = 1 - x - x^4 - x^7 - x^10 - 8*x^13 - 27*x^16 - 64*x^19 - 216*x^22 -... - a(n)^3*x^(3*n+1) -...
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PROGRAM
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(PARI) {a(n)=local(B); if(n==0, 1, B=sum(k=0, n\3, a(k)^3*x^(3*k)); polcoeff(1/(1-x*B+x*O(x^n)), n))}
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CROSSREFS
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Cf. A121652; trisections: A121654, A121655, A121656.
Sequence in context: A078012 A135851 A101913 this_sequence A061418 A136423 A078932
Adjacent sequences: A121650 A121651 A121652 this_sequence A121654 A121655 A121656
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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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