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A307505 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. 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,10
LINKS
FORMULA
T(n,k) = 0 if n+k is odd.
EXAMPLE
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;
...
MAPLE
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);
CROSSREFS
Bisection (even part) of column k=0 gives A307506.
Row sums give A000009.
Main diagonal gives A050315.
Cf. A050314.
Sequence in context: A340999 A119395 A087476 * A035162 A121454 A025462
KEYWORD
nonn,tabl,look,base
AUTHOR
Alois P. Heinz, Apr 11 2019
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)