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A011731 A binary m-sequence: expansion of reciprocal of x^18 + x^7 + 1 (mod 2, shifted by 17 initial 0's). 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Periodic with period of length 2^18 - 1 = 262143. - 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 262143.

FORMULA

G.f. = x^17/(x^18 + x^7 + 1), over GF(2). - M. F. Hasler, Feb 17 2018

PROG

(PARI) A=matrix(N=18, N, i, j, if(i>1, i==j+1, setsearch([7, N], j)>0))*Mod(1, 2); a(n)=lift((A^(n-#A+1))[1, 1]) \\ M. F. Hasler, Feb 17 2018

CROSSREFS

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

Sequence in context: A181838 A185709 A011732 * A085980 A023974 A277164

Adjacent sequences:  A011728 A011729 A011730 * A011732 A011733 A011734

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Edited by M. F. Hasler, Feb 17 2018

STATUS

approved

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Last modified August 18 15:54 EDT 2019. Contains 326108 sequences. (Running on oeis4.)