A110037 - OEIS

%I #4 Mar 30 2012 18:36:49

%S 1,1,-1,0,0,1,0,-1,0,1,-1,0,1,0,0,-1,0,1,-1,0,0,1,0,-1,1,0,-1,0,1,0,0,

%T -1,0,1,-1,0,0,1,0,-1,0,1,-1,0,1,0,0,-1,1,0,-1,0,0,1,0,-1,1,0,-1,0,1,

%U 0,0,-1,0,1,-1,0,0,1,0,-1,0,1,-1,0,1,0,0,-1,0,1,-1,0,0,1,0,-1,1,0,-1,0,1,0,0,-1,1,0,-1,0,0,1,0,-1,0

%N Signed version of A090678 and congruent to A088567 mod 2.

%C 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).

%F 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)).

%o (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)}

%Y Cf. A110036, A090678, A088567.

%K sign

%O 0,1

%A _Paul D. Hanna_, Jul 09 2005