A182510 a(0)=0, a(1)=1, a(n)=(a(n-1) XOR n) - a(n-2).

0, 1, 3, -1, -8, -2, 0, 9, 1, -1, -12, 0, 24, 21, 3, -9, -28, -2, 8, 29, 1, -9, -32, 0, 56, 33, 3, -9, -24, -2, -8, -23, -47, 7, 84, 112, 0, -75, -109, -1, 68, 110, 0, -67, -111, -1, 64, 112, 0, -63, -13, -1, -40, -18, 0, 73, 113, -1, -172, -144, -8, 85, 115

Offset: 0

Author

Alex Ratushnyak, May 03 2012

Keywords

• sign
• easy

Comments

Conjectures: the sequence contains 8 zeros, and more positive terms than negative.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A182509.

Programs

PARI

v=vector(100);v[1]=0;v[2]=1;for(i=3,#v,v[i]=bitxor(v[i-1],i-1)-v[i-2]); v \\ Charles R Greathouse IV, May 03 2012

Python

prpr = 0
prev = 1
for n in range(2,99):
  current = (prev ^ n) - prpr
  print(prpr, end=' ')
  prpr = prev
  prev = current

Formula

a(0)=0, a(1)=1, a(n)=(a(n-1) XOR n) - a(n-2), where XOR is the bitwise exclusive-or operator.