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A112107
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G.f. A(x) satisfies A(A(A(x))) = B(x) (3-rd self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3}, with B(0) = 0.
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3
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1, 1, -1, 3, -10, 35, -119, 360, -792, -33, 12779, -82525, 305861, -552011, -126321, -8385020, 138177591, -433073834, -5366414982, 51203452090, 123835509276, -4174647911014, 5274854624423, 373574363131841, -2054088594386738, -34047892948849106, 391005463740951942
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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EXAMPLE
| A(x) = x + x^2 - x^3 + 3*x^4 - 10*x^5 + 35*x^6 - 119*x^7 +...
where A(A(A(x)))) = x + 3*x^2 + 3*x^3 + 3*x^4 + 2*x^5 +...
is the g.f. of A112106.
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PROG
| (PARI) {a(n, m=3)=local(F=x+x^2+x*O(x^n), G); if(n<1, 0, for(k=3, n, G=F+x*O(x^k); for(i=1, m-1, G=subst(F, x, G)); F=F-((polcoeff(G, k)-1)\m)*x^k); return(polcoeff(F, n, x)))}
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CROSSREFS
| Cf. A112106, A112104, A112105, A112108-A112127.
Sequence in context: A099907 A128735 A159309 * A187925 A094855 A081567
Adjacent sequences: A112104 A112105 A112106 * A112108 A112109 A112110
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KEYWORD
| sign
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 27 2005
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