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

Author

Paul D. Hanna, Oct 29 2004

Keywords

• nonn

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

Crossrefs

Cf. A099884, A099887.

Programs

PARI

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

Formula

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