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%I #23 Feb 23 2018 11:55:44
%S 1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,1,1,0,0,0,0,1,1,1,0,0,1,1,0,1,1,1,1,1,
%T 0,1,0,0,0,1,0,0,1,0,1,0,1,1,0,0,0,0,1,1,1,0,0,1,1,0,1,1,1,1,1,0,1,0,
%U 0,0,1,0,0,1,0,1,0,1,1,0,0
%N Expansion of (1 + x^4)/(1 + x + x^3 + x^4 + x^5) mod 2.
%H Muniru A Asiru, <a href="/A011751/b011751.txt">Table of n, a(n) for n = 0..1000</a>
%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), i.e., 31-periodic.
%F a(n+31) = a(n) for all n. - _M. F. Hasler_, Feb 17 2018
%p series((1+x^4)/(1+x+x^3+x^4+x^5),x,100) mod 2;
%p [seq(coeff(series((1+x^4)/(1+x+x^3+x^4+x^5),x,100) mod 2,x,n),n=0..80)]; # _Muniru A Asiru_, Feb 18 2018
%p A011751 := n -> coeftayl((1+x^4)/(1+x+x^3+x^4+x^5),x=0,n) mod 2 # _M. F. Hasler_, Feb 18 2018
%t Mod[ CoefficientList[ Series[(1 + x^4)/(1 + x + x^3 + x^4 + x^5), {x, 0, 105}], x], 2] (* _Robert G. Wilson v_, Feb 19 2018 *)
%o (PARI) a(n)=bittest(1826728215,n%31) \\ _M. F. Hasler_, Feb 17 2018
%Y Cf. A011655..A011750 for other binary m-sequences.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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