cp's OEIS Frontend

A090678 a(n) = A088567(n) mod 2.

%I A090678 #27 Jan 27 2019 14:06:22
%S A090678 1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0,1,
%T A090678 1,0,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,
%U A090678 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 A090678 a(n) = A088567(n) mod 2.
%C A090678 a(n) = -(-1)^[n/2]*A110036(n)/2 for n>=2, where A110036 gives the partial quotients of the continued fraction expansion of 1 + Sum_{n>=0} 1/x^(2^n). - _Paul D. Hanna_, Jul 09 2005
%H A090678 O. J. Rodseth and J. A. Sellers, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL8/Sellers/sellers75.html">On a Restricted m-Non-Squashing Partition Function</a>, Journal of Integer Sequences, Vol. 8 (2005), Article 05.5.4.
%H A090678 N. J. A. Sloane and J. A. Sellers, <a href="https://arxiv.org/abs/math/0312418">On non-squashing partitions</a>, arXiv:math/0312418 [math.CO], 2003.
%H A090678 N. J. A. Sloane and J. A. Sellers, <a href="https://doi.org/10.1016/j.disc.2004.11.014">On non-squashing partitions</a>, Discrete Math., 294 (2005), 259-274.
%F A090678 b(0) == 1; if n is odd, b(n) == b(n-1) + 1; b(8m+2) == 1; b(8m+6) == 0; b(16m+4) == 0; b(16m+12) == 1; for m>0, b(16m) == b(8m), b(32m+8) == 0, b(32m+24) == 1. In other words, for m>0, b(8m) is the value of the bit immediately to the left of the rightmost 1 when m is written in binary.
%F A090678 a(n) = (-1)^floor(n/2)*A110037(n). - _Paul D. Hanna_, Jul 09 2005
%t A090678 nmax = 104; f = 1 + x/(1 - x) + Sum[x^(3*2^(k - 1))/Product[1 - x^(2^j), {j, 0, k}], {k, 1, Log[2, nmax]}];
%t A090678 a[n_] := Mod[SeriesCoefficient[f, {x, 0, n}], 2];
%t A090678 Table[a[n], {n, 0, nmax}] (* _Jean-François Alcover_, Jul 26 2018 *)
%o A090678 (PARI) {a(n)=(-1)^(n\2)*polcoeff(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)} /* _Paul D. Hanna_ */
%Y A090678 b(8m) is (apart from the first term) A038189(m).
%Y A090678 Cf. A110036, A110037.
%K A090678 nonn
%O A090678 0,1
%A A090678 _N. J. A. Sloane_, Dec 20 2003