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A143045
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G.f.: A(x) = x + A(-x)^2.
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4
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1, 1, -2, -3, 10, 18, -68, -131, 530, 1062, -4476, -9198, 39844, 83332, -368136, -780003, 3497058, 7483806, -33940940, -73210874, 335103340, 727473084, -3355045304, -7322240718, 33982884884, 74498594492, -347600543192, -764936992764, 3585459509640, 7916276980872, -37253166379536
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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FORMULA
| G.f. satisfies: A(x) = x + ( x - A(x)^2 )^2. G.f. satisfies: [A(x)^3 - A(-x)^3]/2 = x*[A(x) + A(-x)]/2.
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EXAMPLE
| A(x) = x + x^2 - 2*x^3 - 3*x^4 + 10*x^5 + 18*x^6 - 68*x^7 - 131*x^8 +...
A(x)^2 = x^2 + 2*x^3 - 3*x^4 - 10*x^5 + 18*x^6 + 68*x^7 - 131*x^8 - 530*x^9 +...
A(x)^3 = x^3 + 3*x^4 - 3*x^5 - 20*x^6 + 18*x^7 + 153*x^8 - 131*x^9 -++-...
Note that a bisection of A^3 equals a bisection of A.
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PROG
| (PARI) {a(n)=local(A=x+x^2); for(i=0, n, A=x+subst(A, x, (-x+x*O(x^n)))^2); polcoeff(A, n)}
(PARI) {a(n)=local(A=x+x*O(x^n)); for(i=0, n, A = x + x^2 - 2*x*A^2 + A^4); polcoeff(A, n)}
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CROSSREFS
| Sequence in context: A147673 A057507 A163467 * A156909 A175569 A122822
Adjacent sequences: A143042 A143043 A143044 * A143046 A143047 A143048
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KEYWORD
| sign
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jul 19 2008, Jul 20 2008
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