A011746 - OEIS

%I #28 Jan 12 2024 06:55:41

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

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

%H Michael Gilleland, <a href="/selfsimilar.html">Some Self-Similar Integer Sequences</a>

%H 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 <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 a(n) = A088002(n) mod 2. - _R. J. Mathar_, May 26 2008

%F 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 a(n) = A011662(n-1). - _R. J. Mathar_, Jan 12 2024

%p series((1+x^2)/(1+x^2+x^5),x,100) mod 2;

%t Mod[CoefficientList[Series[(1+x^2)/(1+x^2+x^5),{x,0,80}],x],2] (* _Harvey P. Dale_, Jul 19 2023 *)

%o (PARI) A011746_vec=Vec((1+x^2)/(1+x^2+x^5)+O(x^31))%2 \\ For illustrative purpose.

%o A011746(n)=bittest(377253537,n%31) \\ _M. F. Hasler_, Feb 17 2018

%Y Cf. A011662.

%Y Cf. A011747..A011751 for similar sequences and A011655 - A011745 for other binary m-sequences.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_