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A093114
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Coefficients of the solution to a functional equation.
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0
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1, -2, -2, -16, 14, 64, -484, -2048, 3798, -7168, 96292, 131072, -1247476, 3964928, -27170632, -67108864, 220816742, -497811456, 993377620, -3758096384, 38457826404, -201938960384, 1217833409416, 1099511627776, -4275253627140
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| G.f. A(x) satisfies A(-4x^2)=A(x)+A(-x), A(4x^2)=-4A(x)A(-x).
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FORMULA
| a(n)*(-4)^n = 2*a(2n) - Paul D. Hanna (pauldhanna(AT)juno.com), Apr 04 2004
Given g.f. A(x), then B(x)=4A(x/4) satisfies 0=f(B(x), B(x^2), B(x^4)) where f(u, v, w)=u^2v+uw-v^2.
Given g.f. A(x), then B(x)=4A(x/4) satisfies B(-x^2)=B(x)+B(-x) and B(x^2)=-B(x)*B(-x).
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PROG
| (PARI) a(n)=local(A, A2, m); if(n<1, 0, A=x+O(x^2); m=1; while(m<=n, m*=2; A2=subst(A, x, -x^2); A=A2/2+sqrt(A2^2/4+subst(A, x, x^2))); polcoeff(A, n)*4^(n-1))
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CROSSREFS
| Sequence in context: A097540 A112327 A152541 * A016740 A193145 A133922
Adjacent sequences: A093111 A093112 A093113 * A093115 A093116 A093117
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Mar 20 2004
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