|
| |
|
|
A101122
|
|
XOR BINOMIAL transform of A101119.
|
|
3
| |
|
|
7, 17, 0, 34, 0, 0, 0, 68, 0, 0, 0, 0, 0, 0, 0, 159, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 257, 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, 514, 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, 0, 0, 0, 0, 0, 0
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| Nonzero terms form A101121 and occur at positions 2^k for k>=0. A101119 equals the nonzero differences of A006519 and A003484. See A099884 for the definition of the XOR BINOMIAL transform.
|
|
|
FORMULA
| a(n) = SumXOR_{k=0..n} (C(n, k)Mod2)*A101119(k), where SumXOR is summation under XOR. A101119(n) = SumXOR_{k=0..n} (C(n, k)Mod2)*a(k). a(2^(n-1)) = A101121(n) for n>=1 and a(k)=0 when k is not a power of 2.
|
|
|
PROG
| (PARI) {a(n)=local(B); B=0; for(i=0, n-1, B=bitxor(B, binomial(n-1, i)%2* (16*2^valuation(n-i, 2)-2^(valuation(n-i, 2)%4)-8*(valuation(n-i, 2)\4)-8))); B}
|
|
|
CROSSREFS
| Cf. A003484, A006519, A101119, A101120, A101121.
Sequence in context: A029498 A129422 A184062 * A090535 A107778 A122735
Adjacent sequences: A101119 A101120 A101121 * A101123 A101124 A101125
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Simon Plouffe (simon.plouffe(AT)gmail.com) and Paul D. Hanna (pauldhanna(AT)juno.com), Dec 02 2004
|
| |
|
|
