A099893 XOR BINOMIAL transform of A006068 (inverse Gray code).

0, 1, 3, 0, 7, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 63, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 127

Offset: 0

Author

Paul D. Hanna, Oct 29 2004

Keywords

• nonn
• mult

Comments

See A099884 for the definitions of the XOR BINOMIAL transform and the XOR difference triangle.

Crossrefs

Cf. A099884, A006068, A099894.

Programs

PARI

{a(n)=local(B);B=0;for(i=0,n,B=bitxor(B,binomial(n,i)%2*A006068(n-i) ));B}

Formula

a(2^n) = 2^(n+1)-1 for n>0, with a(0)=0 and a(k)=0 otherwise. a(n) = SumXOR_{i=0..n} (C(n, i)mod 2)*A006068(n-i) and SumXOR is summation under XOR.