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

1, 1, 2, 6, 18, 61, 220, 822, 3157, 12378, 49345, 199441, 815467, 3367153, 14020938, 58811032, 248260925, 1053893607, 4496248445, 19268100048, 82902438819, 357987967157, 1550951132419, 6739554074740, 29366902576469, 128287060703669

Offset: 0

Author

Paul D. Hanna, Jul 01 2011

Keywords

• nonn

Comments

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

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 18*x^4 + 61*x^5 + 220*x^6 +...
The g.f. A(x) satisfies:
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 +...
where the powers of A(x) are given by A003188, which begins:
[0,1,3,2,6,7,5,4,12,13,15,14,10,11,9,8,24,25,27,26,30,31,29,...].
		

Crossrefs

Cf. A003188, A191769.

Programs

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)}