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
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 14 2013
STATUS
approved