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).

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, 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, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0

Offset

0,1

Comments

Periodic with period 2^32-1 = 3*5*17*257*65537 = 4294967295. - 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

Table of n, a(n) for n=0..80.

Index entries for linear recurrences with constant coefficients, order 4294967295.

Index entries for periodic sequences with large period.

Mathematica

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 *)

Prog

(PARI) A011745_vec=concat([1..31]*0, Vec(1/(x^32+x^28+x^27+x+1)+O(x^99))%2)
A=matrix(N=32, N, i, j, if(i>1, i==j+1, setsearch([1, 27, 28, N], j)))*Mod(1, 2);
A011745(n)=lift((A^(n-#A+1))[1, 1]) \\ M. F. Hasler, Feb 17 2018

Crossrefs

Cf. A011655..A011744 for other binary m-sequences, and A011746..A011751 for similar expansions over GF(2).

Sequence in context: A322438 A304572 A070204 * A011744 A358754 A354996

Adjacent sequences: A011742 A011743 A011744 * A011746 A011747 A011748

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Edited by M. F. Hasler, Feb 17 2018

Status

approved