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.

1, 1, 2, 4, 6, 9, 23, 47, 65, 70, 111, 323, 902, 2064, 3997, 6697, 9638, 11664, 11804, 11436, 18903, 61053, 209236, 623648, 1610326, 3685365, 7673031, 14926689, 27784642, 50202979, 88022528, 147757232, 232939294, 338735927, 448199945, 534600063, 571408283, 546281026, 475461610

Offset: 0

Author

Paul D. Hanna, Jul 14 2013

Keywords

• nonn

Comments

A(-1/2) = Sum_{n>=0} (-1)^n / 2^(n + A003188(n)) = 0.75073331594540770872470210...

Examples

			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 +...
where
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 +...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..1024

Crossrefs

Cf. A227527, A003188.

Programs

PARI

{a(n)=polcoeff(sum(m=0, n, x^m*(1+x+x*O(x^n))^bitxor(m,m\2)), n)}
for(n=0, 64, print1(a(n), ", "))

PARI

{a(n) = sum(k=0, n, binomial(bitxor(k,k\2), n-k))}
for(n=0, 64, print1(a(n), ", "))

Formula

a(n) = Sum_{k=0..n} binomial(A003188(k), n-k), where A003188(k) = k XOR [k/2].