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A099887
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XOR difference triangle of the powers of 3, read by rows.
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1
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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.
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FORMULA
| T(n, k) = SumXOR_{i=0..k} (C(k, i)mod 2)*3^i, where SumXOR is the analogue of summation under the binary XOR operation and C(k, i)mod 2 = A047999(k, i).
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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],...
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PROG
| (PARI) T(n, k)=local(B); B=0; for(i=0, k, B=bitxor(B, binomial(k, i)%2*3^(n-i))); B
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CROSSREFS
| Cf. A099884, A047999, A099888.
Sequence in context: A199455 A197831 A152049 * A038220 A053151 A053088
Adjacent sequences: A099884 A099885 A099886 * A099888 A099889 A099890
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KEYWORD
| nonn,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Oct 28 2004
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