A099888 XOR BINOMIAL transform of the powers of 3.

1, 2, 8, 16, 80, 160, 640, 2784, 6560, 21824, 65280, 131072, 524800, 1056192, 4201728, 8408000, 43046720, 86135424, 361186816, 1467183104, 3443838080, 11367226112, 32550397696, 70111011712, 282403304960, 569106797952

Offset

0,2

Comments

The diagonal of the XOR difference triangle A099887. The XOR BINOMIAL transform of this sequence returns the powers of 3. See A099884 for the definitions of the XOR BINOMIAL transform and the XOR difference triangle.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..1024

Formula

a(n) = SumXOR_{k=0..n} (C(n, k) mod 2)*3^k, where SumXOR is summation under XOR.

Prog

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

Crossrefs

Cf. A099884, A099887.

Sequence in context: A354275 A195798 A100736 * A249308 A353820 A199043

Adjacent sequences: A099885 A099886 A099887 * A099889 A099890 A099891

Keyword

nonn

Author

Paul D. Hanna, Oct 29 2004

Status

approved