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A168081 Lucas sequence U_n(x,1) over the field GF(2). 8
0, 1, 2, 5, 8, 21, 34, 81, 128, 337, 546, 1301, 2056, 5381, 8706, 20737, 32768, 86273, 139778, 333061, 526344, 1377557, 2228770, 5308753, 8388736, 22085713, 35782690, 85262357, 134742024, 352649221, 570556418, 1359020033, 2147483648 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The Lucas sequence U_n(x,1) over the field GF(2)={0,1} is: 0, 1, x, x^2+1, x^3, x^4+x^2+1, x^5+x, ... Numerical values are obtained evaluating these 01-polynomials at x=2 over the integers.

The counterpart sequence is V_n(x,1) = x*U_n(x,1) that implies identities like U_{2n}(x,1) = x*U_n(x,1)^2. - Max Alekseyev, Nov 19 2009

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

For n>1, a(n) = (2*a(n-1)) XOR a(n-2).

a(n) = A248663(A206296(n)). - Antti Karttunen, Dec 11 2015

MATHEMATICA

a[0] = 0; a[1] = 1; a[n_] := a[n] = BitXor[2 a[n - 1], a[n - 2]]; Table[a@ n, {n, 0, 32}] (* Michael De Vlieger, Dec 11 2015 *)

PROG

(PARI) { a=0; b=1; for(n=1, 50, c=bitxor(2*b, a); a=b; b=c; print1(c, ", "); ) }

CROSSREFS

A bisection of A006921. Cf. A260022. - N. J. A. Sloane, Jul 14 2015

See also A257971, first differences of A006921. - Reinhard Zumkeller, Jul 14 2015

Cf. A000129, A206296, A248663.

Sequence in context: A092446 A087077 A200276 * A340399 A117647 A121568

Adjacent sequences:  A168078 A168079 A168080 * A168082 A168083 A168084

KEYWORD

nonn

AUTHOR

Max Alekseyev, Nov 18 2009

STATUS

approved

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Last modified June 16 13:56 EDT 2021. Contains 345057 sequences. (Running on oeis4.)