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Search: id:A099894
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| 1, 2, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 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, 64
(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) for n>0, with a(0)=1, and a(k)=0 otherwise. a(n) = SumXOR_{i=0..n} (C(n, i)mod 2)*A038712(n-i) and SumXOR is summation under XOR.
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EXAMPLE
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XOR difference triangle of A038712 begins:
[1],
[3,2],
[1,2,0],
[7,6,4,4],
[1,6,0,4,0],
[3,2,4,4,0,0],
[1,2,0,4,0,0,0],
[15,14,12,12,8,8,8,8],...
where A038712 is in the left-most column and A099894 (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*A038712(n-i) )); B}
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CROSSREFS
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Cf. A099884, A038712, A099895.
Cf. A048298. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 02 2008]
Sequence in context: A135433 A104774 A087263 this_sequence A048298 A123565 A081120
Adjacent sequences: A099891 A099892 A099893 this_sequence A099895 A099896 A099897
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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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