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A307505
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Number T(n,k) of partitions of n into distinct parts whose bitwise XOR equals k; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
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3
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1, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 1, 0, 4, 0, 1, 0, 1, 0, 0, 0, 4, 0, 1, 0, 2, 1, 0, 1, 0, 5, 0, 0, 0, 1, 0, 2, 0, 0, 0, 4, 0, 2, 0, 1, 0, 0, 0, 5, 1, 0, 5, 0, 0, 0, 2, 0, 1, 0, 4, 0, 2
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OFFSET
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0,10
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LINKS
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FORMULA
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T(n,k) = 0 if n+k is odd.
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EXAMPLE
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Triangle T(n,k) begins:
1;
0, 1;
0, 0, 1;
0, 0, 0, 2;
0, 0, 1, 0, 1;
0, 1, 0, 0, 0, 2;
1, 0, 0, 0, 1, 0, 2;
0, 0, 0, 0, 0, 0, 0, 5;
0, 0, 0, 0, 1, 0, 4, 0, 1;
0, 1, 0, 0, 0, 4, 0, 1, 0, 2;
1, 0, 1, 0, 5, 0, 0, 0, 1, 0, 2;
...
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MAPLE
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b:= proc(n, i, k) option remember; `if`(n=0, x^k, `if`(i<1, 0,
b(n, i-1, k)+b(n-i, min(n-i, i-1), Bits[Xor](i, k))))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..n))(b(n$2, 0)):
seq(T(n), n=0..14);
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CROSSREFS
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Bisection (even part) of column k=0 gives A307506.
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KEYWORD
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AUTHOR
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STATUS
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approved
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