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

0,3

Comments

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

Links

Table of n, a(n) for n=0..64.

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.

Prog

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

Crossrefs

Cf. A099884, A006068, A099894.

Sequence in context: A002043 A171002 A137436 * A135534 A346516 A337767

Adjacent sequences: A099890 A099891 A099892 * A099894 A099895 A099896

Keyword

nonn,mult

Author

Paul D. Hanna, Oct 29 2004

Status

approved