0,1

a(n) = (-1)^[n/2]*A090678(n) = A088567(n) mod 2, where A088567(n) equals the number of "non-squashing" partitions of n. a(n) = -A110036(n)/2 for n>=2, where the A110036 gives the partial quotients of the continued fraction expansion of 1 + Sum_{n>=0} 1/x^(2^n).

G.f.: A(x) = 1+x - x^2*(1+x)/(1+x^2) + Sum_{k>=1} x^(3*2^(k-1))/Product_{j=0..k} (1+x^(2^j)).

(PARI) {a(n)=polcoeff(A=1+x-x^2*(1+x)/(1+x^2)+ sum(k=1, #binary(n), x^(3*2^(k-1))/prod(j=0, k, 1+x^(2^j)+x*O(x^n))), n)}

Cf. A110036, A090678, A088567.

Sequence in context: A115359 A117906 A090678 this_sequence A128810 A123272 A091219

Adjacent sequences: A110034 A110035 A110036 this_sequence A110038 A110039 A110040

sign

Paul D. Hanna (pauldhanna(AT)juno.com), Jul 09 2005