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
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],...
Programs
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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).
Comments