login
A374985
Array read by antidiagonals: T(n,k) is the number of n X k matrices whose values cover an initial interval of positive integers and whose rows and columns have values which are strictly increasing.
3
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 11, 11, 1, 1, 1, 1, 45, 197, 45, 1, 1, 1, 1, 197, 4593, 4593, 197, 1, 1, 1, 1, 903, 126289, 732963, 126289, 903, 1, 1, 1, 1, 4279, 3888343, 155242003, 155242003, 3888343, 4279, 1, 1, 1, 1, 20793, 130016393, 40007492715, 289599115433, 40007492715, 130016393, 20793, 1, 1
OFFSET
0,13
LINKS
R. A. Sulanke, Generalizing Narayana and Schroeder Numbers to Higher Dimensions, Electron. J. Combin. 11 (2004), Research Paper 54.
FORMULA
T(n,k) = T(k,n).
EXAMPLE
Array begins:
=====================================================================
n/k | 0 1 2 3 4 5 6 ...
----+----------------------------------------------------------------
0 | 1 1 1 1 1 1 1 ...
1 | 1 1 1 1 1 1 1 ...
2 | 1 1 3 11 45 197 903 ...
3 | 1 1 11 197 4593 126289 3888343 ...
4 | 1 1 45 4593 732963 155242003 40007492715 ...
5 | 1 1 197 126289 155242003 289599115433 723253222084867 ...
6 | 1 1 903 3888343 40007492715 723253222084867 ...
...
The T(2,3) = 11 matrices are:
[1 2 3] [1 2 3] [1 2 3] [1 2 3] [1 2 4] [1 2 4]
[2 3 4] [2 4 5] [3 4 5] [4 5 6] [2 3 5] [3 4 5]
.
[1 2 4] [1 2 5] [1 3 4] [1 3 4] [1 3 5]
[3 5 6] [3 4 6] [2 4 5] [2 5 6] [2 4 6]
PROG
(PARI) \\ See PARI link in A374514 for program code.
for(n=0, 7, print(vector(7, k, A374985(n, k-1))))
CROSSREFS
Columns k=1..4 are A000012, A001003, A105124, A374985.
Main diagonal is A374514.
Cf. A060854 (case all values also distinct).
Sequence in context: A361948 A180172 A327372 * A328323 A090751 A344759
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Sep 16 2024
STATUS
approved