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A112114
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Unique sequence of numbers {1,2,3,...,7} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (7-th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.
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3
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1, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 5, 3, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 7, 4, 7, 4, 4, 4, 3, 2, 5, 3, 1, 1, 7, 5, 2, 4, 2, 2, 1, 2, 6, 5, 1, 5, 7, 7, 7, 7, 5, 6, 5, 6, 4, 1, 6, 1, 2, 7, 1, 5, 3, 7, 2, 4, 4, 4, 3, 2, 4, 5, 7, 7, 3, 1, 2, 3, 5, 5, 6, 4, 7, 6, 1, 6, 5, 2, 1, 1, 6, 1, 4, 3, 1, 2, 3, 3, 3, 7, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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EXAMPLE
| G.f.: A(x) = x + 7*x^2 + 7*x^3 + 7*x^4 + 7*x^5 + 7*x^6 + 7*x^7 +...
then A(x) = B(B(B(B(B(B(B(x))))))) where
B(x) = x + x^2 - 5*x^3 + 43*x^4 - 443*x^5 + 4957*x^6 - 57281*x^7 +...
is the g.f. of A112115.
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PROG
| (PARI) {a(n, m=7)=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); G=F+x*O(x^n); for(i=1, m-1, G=subst(F, x, G)); return(polcoeff(G, n, x)))}
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CROSSREFS
| Cf. A112115, A112104-A112113, A112116-A112127.
Sequence in context: A103983 A195413 A083947 * A031182 A106705 A010727
Adjacent sequences: A112111 A112112 A112113 * A112115 A112116 A112117
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 27 2005
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