A303476 Square array T(n, k) read by antidiagonals, n > 0 and k > 0: T(n, k) is the number of distinct shuffles of the words corresponding to the binary representations of n and of k.

1, 2, 2, 1, 2, 1, 3, 3, 3, 3, 2, 3, 1, 3, 2, 2, 4, 6, 6, 4, 2, 1, 3, 3, 3, 3, 3, 1, 4, 4, 3, 7, 7, 3, 4, 4, 3, 4, 1, 6, 4, 6, 1, 4, 3, 3, 6, 10, 10, 6, 6, 10, 10, 6, 3, 2, 4, 6, 4, 4, 3, 4, 4, 6, 4, 2, 3, 6, 6, 9, 11, 4, 4, 11, 9, 6, 6, 3, 2, 4, 3, 7, 8, 10, 1

Offset

1,2

Comments

A shuffle of two words is formed by interspersing their characters into a new word, keeping the characters of each word in order. Leading zeros are ignored.

Links

Table of n, a(n) for n=1..85.

Rémy Sigrist, C++ program for A303476

Formula

T(n, k) = T(k, n).

T(n, n) = A193020(n).

Apparently T(n, 1) = A008687(n + 1).

T(2^i, 2^j) = 1 + max(i, j) for any i >=0 and j >= 0.

T(n, k) = 1 iff n = 2^i - 1 and k = 2^j - 1 for some i > 0 and j > 0.

T(2^i, 2^j - 1) = binomial(i + j, j) for any i >= 0 and j > 0.

Example

Array T(n, k) begins:
  n\k|   1   2   3   4   5   6   7   8   9  10  11  12
  ---+------------------------------------------------
    1|   1   2   1   3   2   2   1   4   3   3   2   3
    2|   2   2   3   3   4   3   4   4   6   4   6   4
    3|   1   3   1   6   3   3   1  10   6   6   3   6
    4|   3   3   6   3   7   6  10   4   9   7  13   6
    5|   2   4   3   7   4   6   4  11   8   8   6  10
    6|   2   3   3   6   6   3   4  10  12   7   9   6
    7|   1   4   1  10   4   4   1  20  10  10   4  10
    8|   4   4  10   4  11  10  20   4  13  11  24  10
    9|   3   6   6   9   8  12  10  13   9  15  14  18
   10|   3   4   6   7   8   7  10  11  15   8  14  11

Prog

(C++) See Links section.

Crossrefs

Cf. A008687, A193020.

Sequence in context: A343190 A256132 A340057 * A187201 A262403 A343491

Adjacent sequences: A303473 A303474 A303475 * A303477 A303478 A303479

Keyword

nonn,base,tabl

Author

Rémy Sigrist, Apr 24 2018

Status

approved