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
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
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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.
Comments