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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
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, ", "); ) }
(Python)
def A168081(n): return sum(int(not r & ~(2*n-1-r))*2**(n-1-r) for r in range(n)) # Chai Wah Wu, Jun 20 2022
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
Sequence in context: A092446 A087077 A200276 * A340399 A117647 A121568
KEYWORD
nonn
AUTHOR
Max Alekseyev, Nov 18 2009
STATUS
approved

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Last modified March 29 03:39 EDT 2024. Contains 371264 sequences. (Running on oeis4.)