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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.)