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A227526 G.f.: Sum_{n>=0} x^n * (1+x)^A003188(n), where A003188(n) = n XOR [n/2] is the Gray code for n.

%I A227526 #16 Jul 14 2013 14:36:33
%S A227526 1,1,2,4,6,9,23,47,65,70,111,323,902,2064,3997,6697,9638,11664,11804,
%T A227526 11436,18903,61053,209236,623648,1610326,3685365,7673031,14926689,
%U A227526 27784642,50202979,88022528,147757232,232939294,338735927,448199945,534600063,571408283,546281026,475461610
%N A227526 G.f.: Sum_{n>=0} x^n * (1+x)^A003188(n), where A003188(n) = n XOR [n/2] is the Gray code for n.
%C A227526 A(-1/2) = Sum_{n>=0} (-1)^n / 2^(n + A003188(n)) = 0.75073331594540770872470210...
%H A227526 Paul D. Hanna, <a href="/A227526/b227526.txt">Table of n, a(n) for n = 0..1024</a>
%F A227526 a(n) = Sum_{k=0..n} binomial(A003188(k), n-k), where A003188(k) = k XOR [k/2].
%e A227526 G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 6*x^4 + 9*x^5 + 23*x^6 + 47*x^7 + 65*x^8 +...
%e A227526 where
%e A227526 A(x) = 1 + x*(1+x) + x^2*(1+x)^3 + x^3*(1+x)^2 + x^4*(1+x)^6 + x^5*(1+x)^7 + x^6*(1+x)^5 + x^7*(1+x)^4 + x^8*(1+x)^12 + x^9*(1+x)^13 + x^10*(1+x)^15 + x^11*(1+x)^14 + x^12*(1+x)^10 + x^13*(1+x)^11 + x^14*(1+x)^9 + x^15*(1+x)^8 +...
%o A227526 (PARI) {a(n)=polcoeff(sum(m=0, n, x^m*(1+x+x*O(x^n))^bitxor(m,m\2)), n)}
%o A227526 for(n=0, 64, print1(a(n), ", "))
%o A227526 (PARI) {a(n) = sum(k=0, n, binomial(bitxor(k,k\2), n-k))}
%o A227526 for(n=0, 64, print1(a(n), ", "))
%Y A227526 Cf. A227527, A003188.
%K A227526 nonn
%O A227526 0,3
%A A227526 _Paul D. Hanna_, Jul 14 2013