A271710 Table T(n,k) = 2^n XOR 2^k read by antidiagonals, where XOR is the binary exclusive or operator.

0, 3, 3, 5, 0, 5, 9, 6, 6, 9, 17, 10, 0, 10, 17, 33, 18, 12, 12, 18, 33, 65, 34, 20, 0, 20, 34, 65, 129, 66, 36, 24, 24, 36, 66, 129, 257, 130, 68, 40, 0, 40, 68, 130, 257, 513, 258, 132, 72, 48, 48, 72, 132, 258, 513, 1025, 514, 260, 136, 80, 0, 80, 136, 260

Offset: 0

Author

Peter Kagey, Apr 12 2016

Keywords

• nonn
• tabl
• easy

Comments

n > 1 is in this sequence if and only if it is in A018900.

Examples

			a(0) = T(0, 0) = 2^0 XOR 2^0 = 0.
a(1) = T(1, 0) = 2^1 XOR 2^0 = 3.
   0,   3,   5,   9,  17,  33,  65, 129, 257, 513,1025,
   3,   0,   6,  10,  18,  34,  66, 130, 258, 514,1026,
   5,   6,   0,  12,  20,  36,  68, 132, 260, 516,1028,
   9,  10,  12,   0,  24,  40,  72, 136, 264, 520,1032,
  17,  18,  20,  24,   0,  48,  80, 144, 272, 528,1040,
  33,  34,  36,  40,  48,   0,  96, 160, 288, 544,1056,
  65,  66,  68,  72,  80,  96,   0, 192, 320, 576,1088,
 129, 130, 132, 136, 144, 160, 192,   0, 384, 640,1152,
 257, 258, 260, 264, 272, 288, 320, 384,   0, 768,1280,
 513, 514, 516, 520, 528, 544, 576, 640, 768,   0,1536,
1025,1026,1028,1032,1040,1056,1088,1152,1280,1536,   0,
		

Links

• Peter Kagey, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A271709.

Programs

Maple

read("transforms") ;
A271710 := proc(n,k)
    XORnos(2^n,2^k) ;
end proc: # R. J. Mathar, Apr 15 2016

Mathematica

Table[BitXor[2^(n - k), 2^k], {n, 0, 10}, {k, 0, n}] // Flatten (* Michael De Vlieger, Apr 12 2016 *)

PARI

T(n, k) = bitxor(2^n, 2^k);
matrix(10, 10, n, k, n--; k--; T(n,k)) \\ Michel Marcus, Apr 12 2016

Formula

T(n, k) = 0 if n = k.

T(n, k) = A271709(n, k) if n != k.