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A143554
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G.f. satisfies: A(x) = 1 + x*A(x)^5*A(-x)^4.
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8
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1, 1, 1, 5, 9, 55, 117, 775, 1785, 12350, 29799, 211876, 527085, 3818430, 9706503, 71282640, 184138713, 1366368375, 3573805950, 26735839650, 70625252863, 531838637759, 1416298046436, 10723307329700, 28748759731965
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OFFSET
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0,4
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REFERENCES
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Bousquet, Michel; and Lamathe, Cedric; On symmetric structures of order two. Discrete Math. Theor. Comput. Sci. 10 (2008), 153-176. See Table 1. - From N. J. A. Sloane, Jul 12 2011
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LINKS
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Table of n, a(n) for n=0..24.
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FORMULA
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G.f. satisfies: A(x) = [A(x)*A(-x)] + x*[A(x)*A(-x)]^5.
G.f. satisfies: A(x)*A(-x) = (A(x) + A(-x))/2 = G(x^2) where G(x) = 1 + x*G(x)^9 is the g.f. of A062994.
a(2n) = C(9*n,n)/(8*n+1); a(2n+1) = C(9*n+4,n)*5/(8*n+5).
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EXAMPLE
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G.f.: A(x) = 1 + x + x^2 + 5*x^3 + 9*x^4 + 55*x^5 + 117*x^6 + 775*x^7 +...
Let G(x) = 1 + x*G(x)^9 be the g.f. of A062994, then
G(x^2) = A(x)*A(-x) and A(x) = G(x^2) + x*G(x^2)^5 where
G(x) = 1 + x + 9*x^2 + 117*x^3 + 1785*x^4 + 29799*x^5 + 527085*x^6 +...
G(x)^5 = 1 + 5*x + 55*x^2 + 775*x^3 + 12350*x^4 + 211876*x^5 +...
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PROG
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(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=0, n, A=1+x*A^5*subst(A^4, x, -x)); polcoeff(A, n)}
(PARI) {a(n)=local(m=n\2, p=4*(n%2)+1); binomial(9*m+p-1, m)*p/(8*m+p)}
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CROSSREFS
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Cf. A143338, A143546, A143547, A143550, A143551, A143552, A143553; A062994 (bisection).
Sequence in context: A000324 A123817 A124421 * A222536 A222698 A200440
Adjacent sequences: A143551 A143552 A143553 * A143555 A143556 A143557
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Aug 24 2008
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STATUS
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approved
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