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A099887
XOR difference triangle of the powers of 3, read by rows.
1
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
0,2
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.
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).
EXAMPLE
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],...
PROG
(PARI) T(n, k)=local(B); B=0; for(i=0, k, B=bitxor(B, binomial(k, i)%2*3^(n-i))); B
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Oct 28 2004
STATUS
approved