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A binary m-sequence: expansion of reciprocal of x^31 + x^3 + 1 (mod 2, shifted by 30 initial 0's).
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%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_