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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

Alois P. Heinz, Rows n = 0..360, flattened

Wikipedia, Bitwise operation

Wikipedia, Partition (number theory)

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: A005089 A119395 A087476 * A035162 A121454 A025462

Adjacent sequences:  A307502 A307503 A307504 * A307506 A307507 A307508

KEYWORD

nonn,tabl,look,base

AUTHOR

Alois P. Heinz, Apr 11 2019

STATUS

approved

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Last modified January 22 16:37 EST 2020. Contains 331152 sequences. (Running on oeis4.)