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A223143 G.f. satisfies: A(x)^3 = A(x^2)^3 + 9*x. 2

%I #5 Mar 15 2013 12:00:55

%S 1,3,-6,27,-141,819,-5022,31968,-209202,1398420,-9505854,65499759,

%T -456410943,3210397173,-22763553876,162524220984,-1167359075781,

%U 8429107868541,-61148608627518,445450238075655,-3257116365714831,23896262127268719,-175854177039133998

%N G.f. satisfies: A(x)^3 = A(x^2)^3 + 9*x.

%H Paul D. Hanna, <a href="/A223143/b223143.txt">Table of n, a(n) for n = 0..300</a>

%F G.f.: A(x) = ( 1 + Sum_{n>=0} 9*x^(2^n) )^(1/3).

%e G.f.: A(x)) = 1 + 3*x - 6*x^2 + 27*x^3 - 141*x^4 + 819*x^5 - 5022*x^6 +...

%e where

%e A(x)^3 = 1 + 9*x + 9*x^2 + 9*x^4 + 9*x^8 + 9*x^16 + 9*x^32 +...+ 9*x^(2^n) +...

%o (PARI) {a(n)=local(A=1+x); for(i=1, #binary(n), A=(subst(A, x, x^2)^3+9*x+x*O(x^n))^(1/3)); polcoeff(A, n, x)}

%o for(n=0,30,print1(a(n),", "))

%Y Cf. A223142, A107086, A223026.

%K sign

%O 0,2

%A _Paul D. Hanna_, Mar 15 2013

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