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A011746 Expansion of (1 + x^2)/(1 + x^2 + x^5) mod 2.

%I A011746 #28 Jan 12 2024 06:55:41
%S A011746 1,0,0,0,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,
%T A011746 0,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0,1,
%U A011746 0,1,0,1,1,1,0,1,1,0,0,0,1
%N A011746 Expansion of (1 + x^2)/(1 + x^2 + x^5) mod 2.
%H A011746 Michael Gilleland, <a href="/selfsimilar.html">Some Self-Similar Integer Sequences</a>
%H A011746 R. Gold, <a href="http://dx.doi.org/10.1137/0114079">Characteristic linear sequences and their coset functions</a>, J. SIAM Applied. Math., 14 (1966), 980-985.
%H A011746 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
%F A011746 a(n) = A088002(n) mod 2. - _R. J. Mathar_, May 26 2008
%F A011746 G.f.: (1+x^5+x^7+x^9+x^10+x^11+x^13+x^14+x^18+x^19+x^20+x^21+x^22+x^25+x^26+x^28)/(1-x^31). - _Robert Israel_, May 06 2018
%F A011746 a(n) = A011662(n-1). - _R. J. Mathar_, Jan 12 2024
%p A011746 series((1+x^2)/(1+x^2+x^5),x,100) mod 2;
%t A011746 Mod[CoefficientList[Series[(1+x^2)/(1+x^2+x^5),{x,0,80}],x],2] (* _Harvey P. Dale_, Jul 19 2023 *)
%o A011746 (PARI) A011746_vec=Vec((1+x^2)/(1+x^2+x^5)+O(x^31))%2 \\ For illustrative purpose.
%o A011746 A011746(n)=bittest(377253537,n%31) \\ _M. F. Hasler_, Feb 17 2018
%Y A011746 Cf. A011662.
%Y A011746 Cf. A011747..A011751 for similar sequences and A011655 - A011745 for other binary m-sequences.
%K A011746 nonn,easy
%O A011746 0,1
%A A011746 _N. J. A. Sloane_