%I #14 Feb 23 2018 04:27:51
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,
%T 0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,
%U 0,1,0,0,1,1,0,1,0,0,1,1,0
%N A binary m-sequence: expansion of reciprocal of x^31 + x^3 + 1 (mod 2, shifted by 30 initial 0's).
%C Periodic with period 2^31-1 = 2147483647. - _M. F. Hasler_, Feb 17 2018
%D S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%t Join[Table[0, 30], Mod[CoefficientList[1/(x^31+x^3+1) + O[x]^52, x], 2]] (* _Jean-François Alcover_, Feb 23 2018 *)
%o (PARI) A011744_vec=concat([1..31]*0,Vec(1/(x^32+x^28+x^27+x+1)+O(x^99))%2)
%o A=matrix(31,31,i,j,if(i>1,i==j+1,setsearch([3,31],j)>0))*Mod(1,2);
%o A011744(n)=lift((A^(n-30))[1,1]) \\ _M. F. Hasler_, Feb 17 2018
%Y Cf. A011655, A011656, ..., A011745 for other binary m-sequences, and A011746..A011751 for similar expansions over GF(2).
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_