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A112104 Unique sequence of 1's and 2's where g.f. A(x) satisfies A(x) = B(B(x)) such that B(x) is an integer series, with A(0) = 0. 24
1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Paul D. Hanna, Table of n, a(n) for n = 1..512

EXAMPLE

G.f.: A(x) = x + 2*x^2 + 2*x^3 + x^4 + 2*x^5 + x^6 +...

then A(x) = B(B(x)) where

B(x) = x + x^2 + x^5 - 3*x^6 + 7*x^7 - 10*x^8 - 5*x^9 +...

is the g.f. of A112105.

MATHEMATICA

kmax = 105;

A[x_] := Sum[a[k] x^k, {k, kmax}];

B[x_] := Sum[b[k] x^k, {k, kmax}];

sol = {a[1] -> 1, b[1] -> 1};

Do[Print["k = ", k]; sc = SeriesCoefficient[B[(B[x] /. sol) + O[x]^(k+1)] - A[x], {x, 0, k}] /. sol; r = Reduce[(a[k] == 1 || a[k] == 2) && sc == 0, {a[k], b[k]}, Integers]; sol = Join[r // ToRules, sol], {k, 2, kmax}];

a /@ Range[kmax] /. sol (* Jean-Fran├žois Alcover, Nov 05 2019 *)

PROG

(PARI) {a(n, m=2)=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)))}

CROSSREFS

Cf. A112105, A112106-A112127.

Sequence in context: A264032 A251138 A144462 * A059426 A245977 A082389

Adjacent sequences:  A112101 A112102 A112103 * A112105 A112106 A112107

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Aug 27 2005

STATUS

approved

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Last modified July 5 07:46 EDT 2020. Contains 335462 sequences. (Running on oeis4.)