A215117 - OEIS

%I #7 Aug 03 2012 14:50:05

%S 1,1,1,49,721,17281,452065,13511953,443435185,15816390241,

%T 606861668161,24867738772849,1082158542264721,49785517156216897,

%U 2412544311495241633,122762020478952148177,6542028190536528941425,364254737003651267997985,21146448814786605196994305

%N G.f. A(x) satisfies: A(A(A(A(x)))) = G(x) where G(x) = x + 3*x^2 + x*G(G(G(G(x)))) is the g.f. of A215116.

%F a(n) == 1 (mod 48).

%e G.f.: A(x) = x + x^2 + x^3 + 49*x^4 + 721*x^5 + 17281*x^6 + 452065*x^7 +...

%e Let G(x) = A(A(A(A(x)))):

%e G(x) = x + 4*x^2 + 16*x^3 + 256*x^4 + 4864*x^5 + 111616*x^6 + 2983936*x^7 +...

%e such that G(x) = x + 3*x^2 + x*G(G(G(G(x)))):

%e G(G(G(G(x)))) = x + 16*x^2 + 256*x^3 + 4864*x^4 + 111616*x^5 + 2983936*x^6 +...

%o (PARI) {a(n)=local(A=x+x^2,B=x+4*x^2);for(i=1,n+1,B=x+3*x^2+x*subst(B,x,subst(B,x,subst(B,x,B+x^2*O(x^n)))));

%o for(j=1, n+1, A=round((3*A+subst(B, x, serreverse(subst(A,x,subst(A,x,A+x^2*O(x^n))))))/4));; polcoeff(A, n)}

%o for(n=1, 31, print1(a(n), ", "))

%Y Cf. A215116, A213009, A215115, A215119.

%K nonn

%O 1,4

%A _Paul D. Hanna_, Aug 03 2012