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Search: id:A099895
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| 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; listen)
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OFFSET
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0,2
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COMMENT
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See A099884 for the definitions of the XOR BINOMIAL transform and the XOR difference triangle.
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FORMULA
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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.
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EXAMPLE
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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.
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PROGRAM
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(PARI) {a(n)=local(B); B=0; for(i=0, n, B=bitxor(B, binomial(n, i)%2*A000069(n-i) )); B}
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CROSSREFS
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Cf. A099884, A000069, A099896.
Sequence in context: A094771 A021885 A021289 this_sequence A124222 A111823 A113039
Adjacent sequences: A099892 A099893 A099894 this_sequence A099896 A099897 A099898
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Oct 29 2004
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