A271710 - OEIS

%I #22 Apr 15 2016 13:46:21

%S 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,

%T 65,129,66,36,24,24,36,66,129,257,130,68,40,0,40,68,130,257,513,258,

%U 132,72,48,48,72,132,258,513,1025,514,260,136,80,0,80,136,260

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

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

%H Peter Kagey, <a href="/A271710/b271710.txt">Table of n, a(n) for n = 0..10000</a>

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

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

%e a(0) = T(0, 0) = 2^0 XOR 2^0 = 0.

%e a(1) = T(1, 0) = 2^1 XOR 2^0 = 3.

%e    0,   3,   5,   9,  17,  33,  65, 129, 257, 513,1025,

%e    3,   0,   6,  10,  18,  34,  66, 130, 258, 514,1026,

%e    5,   6,   0,  12,  20,  36,  68, 132, 260, 516,1028,

%e    9,  10,  12,   0,  24,  40,  72, 136, 264, 520,1032,

%e   17,  18,  20,  24,   0,  48,  80, 144, 272, 528,1040,

%e   33,  34,  36,  40,  48,   0,  96, 160, 288, 544,1056,

%e   65,  66,  68,  72,  80,  96,   0, 192, 320, 576,1088,

%e  129, 130, 132, 136, 144, 160, 192,   0, 384, 640,1152,

%e  257, 258, 260, 264, 272, 288, 320, 384,   0, 768,1280,

%e  513, 514, 516, 520, 528, 544, 576, 640, 768,   0,1536,

%e 1025,1026,1028,1032,1040,1056,1088,1152,1280,1536,   0,

%p read("transforms") ;

%p A271710 := proc(n,k)

%p     XORnos(2^n,2^k) ;

%p end proc: # _R. J. Mathar_, Apr 15 2016

%t Table[BitXor[2^(n - k), 2^k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Michael De Vlieger_, Apr 12 2016 *)

%o (PARI) T(n, k) = bitxor(2^n, 2^k);

%o matrix(10, 10, n, k, n--; k--; T(n,k)) \\ _Michel Marcus_, Apr 12 2016

%Y Cf. A271709.

%K nonn,tabl,easy

%O 0,2

%A _Peter Kagey_, Apr 12 2016