|
| |
|
|
A099895
|
|
XOR BINOMIAL transform of A000069 (Odious numbers).
|
|
1
|
|
|
|
1, 3, 5, 0, 9, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 65, 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, 129
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
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)=1 and a(k)=0 otherwise. a(n) = SumXOR_{i=0..n} (C(n, i)mod 2)*A000069(n-i) and SumXOR is summation under XOR.
|
|
|
EXAMPLE
|
XOR difference triangle of A000069 begins:
[1],
[2,3],
[4,6,5],
[7,3,5,0],
[8,15,12,9,9],
[11,3,12,0,9,0],
[13,6,5,9,9,0,0],
[14,3,5,0,9,0,0,0],
[16,30,29,24,24,17,17,17,17],...
where A000069 is in the left-most column,
and this sequence forms the main diagonal.
|
|
|
PROG
|
(PARI) {a(n)=local(B); B=0; for(i=0, n, B=bitxor(B, binomial(n, i)%2*A000069(n-i) )); B}
|
|
|
CROSSREFS
|
Cf. A099884, A000069, A099896.
Sequence in context: A222480 A021289 A200480 * A124222 A200615 A111823
Adjacent sequences: A099892 A099893 A099894 * A099896 A099897 A099898
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Paul D. Hanna, Oct 29 2004
|
|
|
STATUS
|
approved
|
| |
|
|
