login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A099886 XOR binomial transform of A099885. 1
1, 3, 7, 9, 21, 63, 107, 189, 273, 819, 1911, 2457, 5189, 15567, 28123, 46701, 65793, 197379, 460551, 592137, 1381653, 4144959, 7039851, 12434877, 17829905, 53489715, 124809335, 160469145, 340873541, 1022620623, 1840690907 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Many terms of this sequence are equal to 3 times another term! Why? The XOR BINOMIAL transform of this sequence is A099885. A099885 is the central terms of the rows of the XOR difference triangle of the powers of 2 (A099884).
LINKS
FORMULA
a(n) = SumXOR_{k=0..n} SumXOR_{i=0..k\2} (C(n, k)mod 2) * (C(k\2, i) mod 2) * 2^((k+1)\2+k\2-i), where the SumXOR is the analog of summation under XOR and x\y stands for floor(x/y) (see Pari program).
PROG
(PARI) {a(n)=my(B); B=0; for(k=0, n, for(i=0, k\2, B=bitxor(B, binomial(n, k)%2*binomial(k\2, i)%2*2^((k+1)\2+k\2-i) ))); B}
CROSSREFS
Sequence in context: A018458 A029539 A018267 * A118564 A098338 A033958
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 28 2004
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)