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

0,3

Links

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

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 *)

Prog

(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

Crossrefs

Cf. A000217, A145768, A003815.

Sequence in context: A369998 A369606 A325117 * A336841 A189486 A131758

Adjacent sequences: A193229 A193230 A193231 * A193233 A193234 A193235

Keyword

nonn

Author

Franklin T. Adams-Watters, Jul 18 2011

Status

approved