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A099892
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XOR BINOMIAL transform of A003188 (Gray code numbers); also the main diagonal of the XOR difference triangle A099891.
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2
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0, 1, 3, 0, 6, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 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, 96
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| See A099884 for the definitions of the XOR BINOMIAL transform and the XOR difference triangle.
Multiplicative with a(2^e) =3*2^(e-1), a(p^e) = 0 otherwise. David W. Wilson (davidwwilson(AT)comcast.net) Jun 12, 2005.
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FORMULA
| a(2^n) = 3*2^(n-1) for n>0, with a(0)=0, a(1) = 1 and a(k)=0 otherwise. a(n) = SumXOR_{i=0..n} (C(n, i)mod 2)*A003188(n-i), where A003188(k)=bitxor(k, [k/2]) and SumXOR is summation under XOR.
Dirichlet g.f. (2^s+1)/(2^s-2). - R. J. Mathar, Apr 14 2011
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PROG
| (PARI) {a(n)=local(B); B=0; for(i=0, n, B=bitxor(B, binomial(n, i)%2*(bitxor((n-i), (n-i)\2)))); B}
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CROSSREFS
| Cf. A099884, A003188, A099891.
Sequence in context: A009780 A175677 A129502 * A060147 A092731 A201567
Adjacent sequences: A099889 A099890 A099891 * A099893 A099894 A099895
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KEYWORD
| nonn,mult
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Oct 29 2004
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