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Search: id:A099891
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| A099891 |
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XOR difference triangle of A003188 (Gray code numbers), read by rows. |
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+0
2
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| 0, 1, 1, 3, 2, 3, 2, 1, 3, 0, 6, 4, 5, 6, 6, 7, 1, 5, 0, 6, 0, 5, 2, 3, 6, 6, 0, 0, 4, 1, 3, 0, 6, 0, 0, 0, 12, 8, 9, 10, 10, 12, 12, 12, 12, 13, 1, 9, 0, 10, 0, 12, 0, 12, 0, 15, 2, 3, 10, 10, 0, 0, 12, 12, 0, 0, 14, 1, 3, 0, 10, 0, 0, 0, 12, 0, 0, 0, 10, 4, 5, 6, 6, 12, 12, 12, 12, 0, 0, 0, 0, 11, 1
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Main diagonal is A099892, the XOR BINOMIAL transform of A003188. See A099884 for the definitions of the XOR BINOMIAL transform and the XOR difference triangle.
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FORMULA
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T(n, k) = SumXOR_{i=0..k} (C(k, i)mod 2)*(A003188(n-i)), where SumXOR is the analogue of summation under the binary XOR operation, and C(k, i)mod 2 = A047999(k, i). T(2^n, 2^n) = 3*2^(n-1) for n>0, with T(1, 1)=1, and T(k, k)=0 elsewhere.
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EXAMPLE
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Rows begin:
[0],
[1,1],
[3,2,3],
[2,1,3,0],
[6,4,5,6,6],
[7,1,5,0,6,0],
[5,2,3,6,6,0,0],
[4,1,3,0,6,0,0,0],
[12,8,9,10,10,12,12,12,12],...
where A003188 fills the left-most column.
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PROGRAM
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(PARI) {T(n, k)=local(B); B=0; for(i=0, k, B=bitxor(B, binomial(k, i)%2*(bitxor((n-i), (n-i)\2)))); B}
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CROSSREFS
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Cf. A099884, A099889, A099892, A099893.
Sequence in context: A033093 A070032 A096839 this_sequence A096835 A064654 A056564
Adjacent sequences: A099888 A099889 A099890 this_sequence A099892 A099893 A099894
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Oct 29 2004
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