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Search: id:A120595
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| A120595 |
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G.f. satisfies: 13*A(x) = 12 + 27*x + A(x)^4, starting with [1,3,6]. |
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3
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| 1, 3, 6, 36, 249, 1932, 16044, 139500, 1253934, 11558316, 108658902, 1037800920, 10041891132, 98230257636, 969814634424, 9651213968784, 96710160474513, 974967422602428, 9881687141571732, 100632995795535588
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OFFSET
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0,2
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COMMENT
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See comments in A120588 for conditions needed for an integer sequence to satisfy a functional equation of the form: r*A(x) = c + b*x + A(x)^n.
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FORMULA
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G.f.: A(x) = 1 + Series_Reversion((1+13*x - (1+x)^4)/27). Lagrange Inversion yields: G.f.: A(x) = Sum_{n>=0} C(4*n,n)/(3*n+1) * (12+27*x)^(3*n+1)/13^(4*n+1). - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 24 2008
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EXAMPLE
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A(x) = 1 + 3*x + 6*x^2 + 36*x^3 + 249*x^4 + 1932*x^5 +...
A(x)^4 = 1 + 12*x + 78*x^2 + 468*x^3 + 3237*x^4 + 25116*x^5 +...
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PROGRAM
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(PARI) {a(n)=local(A=1+3*x+6*x^2+x*O(x^n)); for(i=0, n, A=A+(-13*A+12+27*x+A^4)/9); polcoeff(A, n)}
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CROSSREFS
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Cf. A120588 - A120594, A120596 - A120607.
Sequence in context: A076983 A068084 A003674 this_sequence A048642 A077532 A093800
Adjacent sequences: A120592 A120593 A120594 this_sequence A120596 A120597 A120598
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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), Jun 16 2006
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