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%I #17 Mar 27 2018 17:26:04
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,1,
%T 0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,
%U 0,1,0,0,1,1,1,1,0,1,1,1,0
%N A binary m-sequence: expansion of reciprocal of x^25 + x^3 + 1 (mod 2, shifted by 24 initial 0's).
%C Sequence is 2^25-1 = 33554431-periodic. - _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.
%H Robert Israel, <a href="/A011738/b011738.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_33554431">Index entries for linear recurrences with constant coefficients</a>, order 33554431.
%H <a href="/index/Per#periodic">Index entries for periodic sequences with large period</a>.
%F G.f. = x^24/(x^25+x^3+1), over GF(2). - _M. F. Hasler_, Feb 17 2018
%p N:= 200: # to get a(0)..a(N)
%p A:= Array(0..N):
%p A[24]:= 1:
%p for n from 25 to N do A[n]:= A[n-3] + A[n-25] mod 2 od:
%p convert(A,list); # _Robert Israel_, Mar 25 2018
%o (PARI) A=matrix(N=25,N,i,j, if(i>1, i==j+1, setsearch([3,N],j)>0))*Mod(1, 2); a(n)=lift((A^(n-#A+1))[1,1]) \\ _M. F. Hasler_, Feb 17 2018
%Y Cf. A011655..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_
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