A213081 Exclusive-or based Pascal triangle, read by rows: T(n,1)=T(n,n)=n and T(n,k) = T(n-1,k-1) XOR T(n-1,k), where XOR is the bitwise exclusive-or operator.

1, 2, 2, 3, 0, 3, 4, 3, 3, 4, 5, 7, 0, 7, 5, 6, 2, 7, 7, 2, 6, 7, 4, 5, 0, 5, 4, 7, 8, 3, 1, 5, 5, 1, 3, 8, 9, 11, 2, 4, 0, 4, 2, 11, 9, 10, 2, 9, 6, 4, 4, 6, 9, 2, 10, 11, 8, 11, 15, 2, 0, 2, 15, 11, 8, 11, 12, 3, 3, 4, 13, 2, 2, 13, 4, 3, 3, 12, 13, 15

Offset: 1

Author

Alex Ratushnyak, Jun 04 2012

Keywords

• nonn
• tabl
• base

Examples

			Table begins:
   1;
   2,  2;
   3,  0,  3;
   4,  3,  3,  4;
   5,  7,  0,  7,  5;
   6,  2,  7,  7,  2,  6;
   7,  4,  5,  0,  5,  4,  7;
   8,  3,  1,  5,  5,  1,  3,  8;
   9, 11,  2,  4,  0,  4,  2, 11,  9;
  10,  2,  9,  6,  4,  4,  6,  9,  2, 10;
  11,  8, 11, 15,  2,  0,  2, 15, 11,  8, 11;
		

Crossrefs

Cf. A007318 - Pascal's triangle read by rows.

Cf. A051597 - Pascal's triangle, begin and end n-th row with n+1, read by rows.

Cf. A080046 - Multiplicative Pascal triangle, read by rows: T(n,1)=T(n,n)=n and T(n,k) = T(n-1,k-1) * T(n-1,k).

Programs

Python

src = [0]*1024
dst = [0]*1024
for i in range(1,39):
    dst[0] = dst[i-1] = i
    for j in range(1,i-1):
        dst[j] = src[j-1]^src[j]
    for j in range(i):
        src[j] = dst[j]
        print(dst[j], end=',')