A193232 Bitwise XOR of first n triangular numbers.

0, 1, 2, 4, 14, 1, 20, 8, 44, 1, 54, 116, 58, 97, 8, 112, 248, 97, 202, 116, 166, 65, 188, 424, 132, 449, 158, 484, 114, 449, 16, 480, 1008, 449, 914, 484, 894, 449, 804, 40, 796, 65, 966, 116, 938, 1953, 920, 2032, 872, 1953, 858, 1652, 790, 1665, 844, 1352

Offset: 0

Author

Franklin T. Adams-Watters, Jul 18 2011

Keywords

• nonn

Links

• John Tyler Rascoe, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000217, A145768, A003815.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 0,
      Bits[Xor](a(n-1), n*(n+1)/2))
    end:
seq(a(n), n=0..55);  # Alois P. Heinz, Feb 19 2023

Mathematica

Module[{nn=60,trs},trs=Accumulate[Range[nn]];Table[BitXor@@Take[trs,n],{n,0,nn}]] (* Harvey P. Dale, Dec 15 2017 *)

PARI

al(n) = local(m); vector(n,k,m=bitxor(m,k*(k+1)\2))

Python

from operator import xor
from functools import reduce
def A193232(n): return reduce(xor, (x*(x+1) for x in range(n+1)))//2 # Chai Wah Wu, Dec 16 2021