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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.
2
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?
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
KEYWORD
nonn,tabl
AUTHOR
Rémy Sigrist, Mar 07 2019
STATUS
approved