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A099893
XOR BINOMIAL transform of A006068 (inverse Gray code).
1
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.
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
KEYWORD
nonn,mult
AUTHOR
Paul D. Hanna, Oct 29 2004
STATUS
approved