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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 27 12:58 EDT 2022. Contains 354097 sequences. (Running on oeis4.)