A112107 G.f. A(x) satisfies A(A(A(x))) = B(x) (3rd self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3}, with B(0) = 0.

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

Offset

1,4

Links

Table of n, a(n) for n=1..27.

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.

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)))}

Crossrefs

Cf. A112106, A112104, A112105, A112108-A112127.

Sequence in context: A128735 A330050 A159309 * A187925 A372852 A094855

Adjacent sequences: A112104 A112105 A112106 * A112108 A112109 A112110

Keyword

sign

Author

Paul D. Hanna, Aug 27 2005

Status

approved