cp's OEIS Frontend

A011745 A binary m-sequence: expansion of reciprocal of x^32 + x^28 + x^27 + x + 1 (mod 2, shifted by 31 initial 0's).

%I A011745 #19 Feb 23 2018 04:26:56
%S A011745 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,
%T A011745 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,
%U A011745 0,1,0,1,0,1,0,1,0,1,0,1,0
%N A011745 A binary m-sequence: expansion of reciprocal of x^32 + x^28 + x^27 + x + 1 (mod 2, shifted by 31 initial 0's).
%C A011745 Periodic with period 2^32-1 = 3*5*17*257*65537 = 4294967295. - _M. F. Hasler_, Feb 17 2018
%D A011745 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011745 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011745 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%H A011745 <a href="/index/Rec#order_4294967295">Index entries for linear recurrences with constant coefficients</a>, order 4294967295.
%H A011745 <a href="/index/Per#periodic">Index entries for periodic sequences with large period</a>.
%t A011745 Join[Table[0, 31], Mod[CoefficientList[1/(x^32 + x^28 + x^27 + x + 1) + O[x]^50, x], 2]] (* _Jean-François Alcover_, Feb 23 2018 *)
%o A011745 (PARI) A011745_vec=concat([1..31]*0,Vec(1/(x^32+x^28+x^27+x+1)+O(x^99))%2)
%o A011745 A=matrix(N=32,N,i,j,if(i>1,i==j+1,setsearch([1,27,28,N],j)))*Mod(1,2);
%o A011745 A011745(n)=lift((A^(n-#A+1))[1,1]) \\ _M. F. Hasler_, Feb 17 2018
%Y A011745 Cf. A011655..A011744 for other binary m-sequences, and A011746..A011751 for similar expansions over GF(2).
%K A011745 nonn,easy
%O A011745 0,1
%A A011745 _N. J. A. Sloane_
%E A011745 Edited by _M. F. Hasler_, Feb 17 2018