A099890 XOR BINOMIAL transform of the odd numbers; also the main diagonal of the XOR difference triangle A099889.

1, 2, 4, 0, 8, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 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, 128

Offset: 0

Author

Paul D. Hanna, Oct 29 2004

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1024

Crossrefs

Cf. A099884, A099889.

Programs

Mathematica

Join[{1},Table[If[IntegerQ[Log2[n]],2n,0],{n,512}]] (* or *) Join[{1},With[{kk=10},Flatten[ Riffle[ 2^Range[kk],Table[PadRight[{},2^k-1,0],{k,0,kk}]]]]] (* Harvey P. Dale, Aug 11 2024 *)

PARI

a(n)=local(B);B=0;for(i=0,n,B=bitxor(B,binomial(n,i)%2*(2*(n-i)+1)));B

Formula

a(0) = 1; a(2^n) = 2^(n+1); a(n) = 0 otherwise.