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

0,3

Comments

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

Links

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

Formula

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

Example

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 +...

Prog

(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), ", "))

Crossrefs

Cf. A227527, A003188.

Sequence in context: A049912 A268868 A271927 * A093081 A242521 A338298

Adjacent sequences: A227523 A227524 A227525 * A227527 A227528 A227529

Keyword

nonn

Author

Paul D. Hanna, Jul 14 2013

Status

approved