A003815 a(0) = 0, a(n) = a(n-1) XOR n.

0, 1, 3, 0, 4, 1, 7, 0, 8, 1, 11, 0, 12, 1, 15, 0, 16, 1, 19, 0, 20, 1, 23, 0, 24, 1, 27, 0, 28, 1, 31, 0, 32, 1, 35, 0, 36, 1, 39, 0, 40, 1, 43, 0, 44, 1, 47, 0, 48, 1, 51, 0, 52, 1, 55, 0, 56, 1, 59, 0, 60, 1, 63, 0, 64, 1, 67, 0

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0, 1, 0, 1, 0, -1).

Formula

a(n) = n + (-1)^n*a(n-1). - Vladeta Jovovic, Mar 13 2003

a(0)=0, a(4n+1)=1, a(4n+2)=4n+3, a(4n+3)=0, a(4n+4)=4n+4, n >= 0.

a(n) = f(n,0) with f(n,x) = x if n=0, otherwise f(n-1,x+n) if x is even, otherwise f(n-1,x-n). - Reinhard Zumkeller, Oct 09 2007

a(n) = abs(A077140(n)) for n > 0. - Reinhard Zumkeller, Oct 09 2007

G.f.: x*(1+3*x-x^2+x^3)/((1-x^4)*(1-x^2)). - Vincenzo Librandi, Oct 12 2013

a(n) = (1 + n + n*(-1)^n + (-1)^floor((n-1)/2))/2. - Wesley Ivan Hurt, May 08 2021

Mathematica

an = 0; Reap[ For[i = 0, i <= 100, i++, an = BitXor[an, i]; Sow[an]]][[2, 1]] (* Jean-François Alcover, Oct 11 2013, translated from PARI *)
CoefficientList[Series[x (1 + 3 x - x^2 + x^3)/((1 - x^4) (1 - x^2)), {x, 0, 100}], x] (* Vincenzo Librandi, Oct 12 2013 *)
nxt[{n_, a_}]:={n+1, BitXor[n+1, a]}; NestList[nxt, {0, 0}, 70][[All, 2]] (* Harvey P. Dale, Mar 10 2019 *)
{#, 1, #+1, 0}[[1+Mod[#, 4]]]&/@Range[0, 100] (* Federico Provvedi, May 10 2021 *)

Prog

(PARI) print1(an=0); for( i=1, 100, print1(", ", an=bitxor(an, i))) \\ M. F. Hasler, Oct 20 2008

Crossrefs

Cf. A003816.

Cf. A077140, A145768. - M. F. Hasler, Oct 20 2008

Sequence in context: A319974 A138376 A077140 * A306562 A351190 A131486

Adjacent sequences: A003812 A003813 A003814 * A003816 A003817 A003818

Keyword

nonn,base

Author

Marc LeBrun

Status

approved