login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 * A117647 A121568 A276464

Adjacent sequences:  A168078 A168079 A168080 * A168082 A168083 A168084

KEYWORD

nonn

AUTHOR

Max Alekseyev, Nov 18 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 17:36 EST 2019. Contains 329865 sequences. (Running on oeis4.)