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Search: id:A099889
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| A099889 |
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XOR difference triangle of the odd numbers, read by rows. |
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+0
3
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| 1, 3, 2, 5, 6, 4, 7, 2, 4, 0, 9, 14, 12, 8, 8, 11, 2, 12, 0, 8, 0, 13, 6, 4, 8, 8, 0, 0, 15, 2, 4, 0, 8, 0, 0, 0, 17, 30, 28, 24, 24, 16, 16, 16, 16, 19, 2, 28, 0, 24, 0, 16, 0, 16, 0, 21, 6, 4, 24, 24, 0, 0, 16, 16, 0, 0, 23, 2, 4, 0, 24, 0, 0, 0, 16, 0, 0, 0, 25, 14, 12, 8, 8, 16, 16, 16, 16, 0
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Main diagonal is A099890, the XOR BINOMIAL transform of the odd numbers. 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)*(2*(n-i)+1), 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) = 2^(n+1) for n>=0, with T(0, 0)=1.
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EXAMPLE
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Rows begin:
[1],
[3,2],
[5,6,4],
[7,2,4,0],
[9,14,12,8,8],
[11,2,12,0,8,0],
[13,6,4,8,8,0,0],
[15,2,4,0,8,0,0,0],
[17,30,28,24,24,16,16,16,16],...
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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*(2*(n-i)+1))); B
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CROSSREFS
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Cf. A099884, A099890.
Sequence in context: A008623 A035546 A134237 this_sequence A115511 A026098 A135764
Adjacent sequences: A099886 A099887 A099888 this_sequence A099890 A099891 A099892
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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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