A099887 XOR difference triangle of the powers of 3, read by rows.

1, 3, 2, 9, 10, 8, 27, 18, 24, 16, 81, 74, 88, 64, 80, 243, 162, 232, 176, 240, 160, 729, 554, 648, 608, 720, 544, 640, 2187, 2642, 2168, 2800, 2192, 2624, 2144, 2784, 6561, 4394, 7032, 4864, 6640, 4448, 6944, 4928, 6560, 19683, 21826, 17512, 24336, 19472

Offset: 0

Author

Paul D. Hanna, Oct 28 2004

Keywords

• nonn
• tabl

Comments

Main diagonal is A099888, the XOR BINOMIAL transform of the powers of 3. See A099884 for the definition of XOR BINOMIAL transform and for the definition of the XOR difference triangle.

Examples

			Rows begin:
[1],
[3,2],
[9,10,8],
[27,18,24,16],
[81,74,88,64,80],
[243,162,232,176,240,160],
[729,554,648,608,720,544,640],
[2187,2642,2168,2800,2192,2624,2144,2784],
[6561,4394,7032,4864,6640,4448,6944,4928,6560],
[19683,21826,17512,24336,19472,21984,17536,24480,19680,21824],...
		

Crossrefs

Cf. A099884, A047999, A099888.

Programs

PARI

T(n,k)=local(B);B=0;for(i=0,k,B=bitxor(B,binomial(k,i)%2*3^(n-i)));B

Formula

T(n, k) = SumXOR_{i=0..k} (C(k, i)mod 2)*3^i, where SumXOR is the analog of summation under the binary XOR operation and C(k, i)mod 2 = A047999(k, i).