A011744 A binary m-sequence: expansion of reciprocal of x^31 + x^3 + 1 (mod 2, shifted by 30 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, 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, 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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Periodic with period 2^31-1 = 2147483647. - 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.

Crossrefs

Cf. A011655, A011656, ..., A011745 for other binary m-sequences, and A011746..A011751 for similar expansions over GF(2).

Programs

Mathematica

Join[Table[0, 30], Mod[CoefficientList[1/(x^31+x^3+1) + O[x]^52, x], 2]] (* Jean-François Alcover, Feb 23 2018 *)

PARI

A011744_vec=concat([1..31]*0,Vec(1/(x^32+x^28+x^27+x+1)+O(x^99))%2)
A=matrix(31,31,i,j,if(i>1,i==j+1,setsearch([3,31],j)>0))*Mod(1,2);
A011744(n)=lift((A^(n-30))[1,1]) \\ M. F. Hasler, Feb 17 2018