login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A binary m-sequence: expansion of reciprocal of x^30 + x^16 + x^15 + x + 1 (mod 2, shifted by 29 initial 0's).
1

%I #10 Feb 17 2018 13:53:40

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

%T 1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,

%U 1,0,1,0,1,0,0,1,0,1,0,1,0

%N A binary m-sequence: expansion of reciprocal of x^30 + x^16 + x^15 + x + 1 (mod 2, shifted by 29 initial 0's).

%C Periodic with length of period 2^30-1. - _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.

%o (PARI) A011743_vec=concat([1..29]*0, Vec(1/(x^30+x^16+x^15+x+1)+O(x^99))%2)

%o A=matrix(30, 30, i, j, if(i>1, i==j+1, setsearch([1,15,16,30], j)>0))*Mod(1, 2);

%o A011743(n)=lift((A^(n-29))[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

%O 0,1

%A _N. J. A. Sloane_