A306741 Square array T(n,k), n > 0, k > 1, read by antidiagonals: T(n, k) = 1 when n <= 2 or k <= 2, T(n, k) = T(n-T(n-1, k-1), k-T(n-2, k-2)) + T(n-T(n-2, k-2), k-T(n-1, k-1)) otherwise.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 3, 3, 2, 1, 1, 1, 1, 2, 3, 4, 3, 2, 1, 1, 1, 1, 2, 3, 3, 3, 3, 2, 1, 1, 1, 1, 2, 3, 3, 2, 3, 3, 2, 1, 1, 1, 1, 2, 3, 3, 4, 4, 3, 3, 2, 1, 1, 1, 1, 2, 3, 3, 4, 4, 4, 3

Offset

1,13

Comments

This sequence is a 2-dimensional variant of A005185.

Is T(n, k) defined for all positive n and k?

Links

Table of n, a(n) for n=1..87.

Rémy Sigrist, Colored representation of T(n, k) for n = 1..1000 and k = 1..1000 (where the hue is function of T(n, k))

Rémy Sigrist, Scatterplot of (n, k) such that T(n, k) is odd for n = 1..1000 and k = 1..1000

Rémy Sigrist, PARI program for A306741

Index entries for Hofstadter-type sequences

Formula

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

Example

Array T(n, k) begins:
  n\k|  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20
  ---+-----------------------------------------------------------------------
    1|  1  1  1  1  1  1  1  1  1   1   1   1   1   1   1   1   1   1   1   1
    2|  1  1  1  1  1  1  1  1  1   1   1   1   1   1   1   1   1   1   1   1
    3|  1  1  2  2  2  2  2  2  2   2   2   2   2   2   2   2   2   2   2   2
    4|  1  1  2  2  3  3  3  3  3   3   3   3   3   3   3   3   3   3   3   3
    5|  1  1  2  3  4  3  3  3  3   3   3   3   3   3   3   3   3   3   3   3
    6|  1  1  2  3  3  2  4  4  4   4   4   4   4   4   4   4   4   4   4   4
    7|  1  1  2  3  3  4  4  4  5   5   5   5   5   5   5   5   5   5   5   5
    8|  1  1  2  3  3  4  4  6  6   5   5   5   5   5   5   5   5   5   5   5
    9|  1  1  2  3  3  4  5  6  4   5   6   6   6   6   6   6   6   6   6   6
   10|  1  1  2  3  3  4  5  5  5   6   7   6   6   6   6   6   6   6   6   6
   11|  1  1  2  3  3  4  5  5  6   7   6   6   6   6   6   6   6   6   6   6
   12|  1  1  2  3  3  4  5  5  6   6   6   4   5   8   8   8   8   8   8   8
   13|  1  1  2  3  3  4  5  5  6   6   6   5  10  11   7   7   8   8   8   8
   14|  1  1  2  3  3  4  5  5  6   6   6   8  11   6   5   8   9   8   8   8
   15|  1  1  2  3  3  4  5  5  6   6   6   8   7   5   6   6  11  10  10  10

Prog

(PARI) See Links section.

Crossrefs

Cf. A005185, A306743 (main diagonal).

Sequence in context: A139038 A322812 A259094 * A274193 A238384 A139040

Adjacent sequences: A306738 A306739 A306740 * A306742 A306743 A306744

Keyword

nonn,tabl

Author

Rémy Sigrist, Mar 07 2019

Status

approved