This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A110037 #9 Aug 24 2025 18:27:45
%S A110037 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 A110037 -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 A110037 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 A110037 Signed version of A090678 and congruent to A088567 mod 2.
%C A110037 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 A110037 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)).
%F A110037 Conjecture: a(n) = A073089(n) - A073089(n+1) for n >= 2. - _Alan Michael Gómez Calderón_, Aug 19 2025
%o A110037 (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 A110037 Cf. A110036, A090678, A088567, A073089.
%K A110037 sign,changed
%O A110037 0,1
%A A110037 _Paul D. Hanna_, Jul 09 2005