

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
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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 01polynomials 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(n1)) XOR a(n2).
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 * A117647 A121568 A276464
Adjacent sequences: A168078 A168079 A168080 * A168082 A168083 A168084


KEYWORD

nonn


AUTHOR

Max Alekseyev, Nov 18 2009


STATUS

approved



