A099890 - OEIS

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

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OFFSET

0,2

LINKS

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

FORMULA

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

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 *)

PROG

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

CROSSREFS

Cf. A099884, A099889.

Sequence in context: A076813 A049289 A258053 * A208745 A137511 A011166

Adjacent sequences: A099887 A099888 A099889 * A099891 A099892 A099893

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 29 2004

STATUS

approved