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

0,2

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.

Links

Table of n, a(n) for n=0..49.

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

Cf. A099884, A047999, A099888.

Sequence in context: A246788 A365278 A342802 * A366348 A274827 A038220

Adjacent sequences: A099884 A099885 A099886 * A099888 A099889 A099890

Keyword

nonn,tabl

Author

Paul D. Hanna, Oct 28 2004

Status

approved