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A101309
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Matrix logarithm of A047999 (Pascal's triangle mod 2).
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1
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0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Row sums equal A000120 (binary 1's-counting sequence). Antidiagonal sums form A101979.
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FORMULA
| T(n, k)=1 when n XOR k = 2^m for integer m>=0, T(n, k)=0 elsewhere.
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EXAMPLE
| T(n,k)=1 when n XOR k is a power of 2:
T(3,2)=1 since 3 XOR 2 = 2^0, T(4,0)=1 since 4 XOR 0 = 2^2,
T(5,1)=1 since 5 XOR 1 = 2^2, T(6,4)=1 since 6 XOR 4 = 2^2.
Rows begin:
[0],
[1, 0],
[1,0, 0],
[0,1, 1,0],
[1,0,0,0, 0],
[0,1,0,0, 1,0],
[0,0,1,0, 1,0,0],
[0,0,0,1, 0,1,1,0],...
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PROG
| (PARI) T(n, k)=if(n>k&bitxor(n, k)==2^valuation(bitxor(n, k), 2), 1, 0)
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CROSSREFS
| Cf. A047999, A101979.
Sequence in context: A157687 A127266 A083923 * A141474 A073424 A135993
Adjacent sequences: A101306 A101307 A101308 * A101310 A101311 A101312
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KEYWORD
| nonn,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Dec 23 2004
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