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Search: id:A143555
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| A143555 |
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G.f. satisfies: A(x) = 1 + x*A(x)^2/A(-x)^2. |
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+0
6
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| 1, 1, 4, 8, 28, 80, 308, 984, 3980, 13472, 56164, 197032, 838396, 3013872, 13015188, 47624568, 207971436, 771336512, 3397886660, 12736715592, 56502898140, 213618833808, 953139545076, 3629043226392, 16270547827020, 62317467147744
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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G.f. satisfies: A(x) = 1 + x^2/(1 - A(-x)).
G.f. satisfies: A(x) = 1 + ( 1 - (1+x^2)/A(x) )^2/x.
G.f. satisfies: (1+x^2)^2 - 2*(1+x^2)*A(x) + (1+x)*A(x)^2 - x*A(x)^3 = 0.
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EXAMPLE
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G.f. A(x) = 1 + x + 4*x^2 + 8*x^3 + 28*x^4 + 80*x^5 + 308*x^6 +...
A(x)/A(-x) = 1 + 2*x + 2*x^2 + 10*x^3 + 18*x^4 + 98*x^5 + 210*x^6 +...
where 1 - (1+x^2)/A(x) = x*A(x)/A(-x).
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PROGRAM
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(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=0, n, A=1+x*A^2/subst(A^2, x, -x)); polcoeff(A, n)}
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CROSSREFS
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Cf. A143554, A143556, A143557, A143558, A143559.
Sequence in context: A034515 A059480 A105723 this_sequence A025234 A075308 A020331
Adjacent sequences: A143552 A143553 A143554 this_sequence A143556 A143557 A143558
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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 24 2008
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