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A192483 G.f.: A(x) = Sum_{n>=0} x^n * A(x)^A003188(n) where A003188(n) = n XOR floor(n/2). 1

%I

%S 1,1,2,6,18,61,220,822,3157,12378,49345,199441,815467,3367153,

%T 14020938,58811032,248260925,1053893607,4496248445,19268100048,

%U 82902438819,357987967157,1550951132419,6739554074740,29366902576469,128287060703669

%N G.f.: A(x) = Sum_{n>=0} x^n * A(x)^A003188(n) where A003188(n) = n XOR floor(n/2).

%C A003188(n) is the decimal equivalent of the binary Gray code for n; A003188 forms a permutation of the nonnegative integers.

%e G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 18*x^4 + 61*x^5 + 220*x^6 +...

%e The g.f. A(x) satisfies:

%e A(x) = 1 + x*A(x) + x^2*A(x)^3 + x^3*A(x)^2 + x^4*A(x)^6 + x^5*A(x)^7 + x^6*A(x)^5 + x^7*A(x)^4 + x^8*A(x)^12 + x^9*A(x)^13 + x^10*A(x)^15 +...

%e where the powers of A(x) are given by A003188, which begins:

%e [0,1,3,2,6,7,5,4,12,13,15,14,10,11,9,8,24,25,27,26,30,31,29,...].

%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=sum(m=0,n,x^m*(A+x*O(x^n))^bitxor(m,m\2)));polcoeff(A,n)}

%Y Cf. A003188, A191769.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jul 01 2011

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Last modified January 25 08:59 EST 2021. Contains 340416 sequences. (Running on oeis4.)