A011738 A binary m-sequence: expansion of reciprocal of x^25 + x^3 + 1 (mod 2, shifted by 24 initial 0'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, 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, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Sequence is 2^25-1 = 33554431-periodic. - M. F. Hasler, Feb 17 2018

References

• S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
• H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
• F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, order 33554431.
• Index entries for periodic sequences with large period.

Crossrefs

Cf. A011655..A011745 for other binary m-sequences, and A011746..A011751 for similar expansions over GF(2).

Programs

Maple

N:= 200: # to get a(0)..a(N)
A:= Array(0..N):
A[24]:= 1:
for n from 25 to N do A[n]:= A[n-3] + A[n-25] mod 2 od:
convert(A,list); # Robert Israel, Mar 25 2018

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

Formula

G.f. = x^24/(x^25+x^3+1), over GF(2). - M. F. Hasler, Feb 17 2018