A288518 Array read by antidiagonals: T(m,n) = number of (undirected) paths in the grid graph P_m X P_n.

0, 1, 1, 3, 12, 3, 6, 49, 49, 6, 10, 146, 322, 146, 10, 15, 373, 1618, 1618, 373, 15, 21, 872, 7119, 14248, 7119, 872, 21, 28, 1929, 28917, 111030, 111030, 28917, 1929, 28, 36, 4118, 111360, 801756, 1530196, 801756, 111360, 4118, 36

Offset: 1

Author

Andrew Howroyd, Jun 10 2017

Keywords

• nonn
• tabl

Comments

Paths of length zero are not counted here.

Examples

			Table starts:
=================================================================
m\n|  1    2      3       4         5          6            7
---|-------------------------------------------------------------
1  |  0    1      3       6        10         15           21 ...
2  |  1   12     49     146       373        872         1929 ...
3  |  3   49    322    1618      7119      28917       111360 ...
4  |  6  146   1618   14248    111030     801756      5493524 ...
5  | 10  373   7119  111030   1530196   19506257    235936139 ...
6  | 15  872  28917  801756  19506257  436619868   9260866349 ...
7  | 21 1929 111360 5493524 235936139 9260866349 343715004510 ...
...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..276
• Eric Weisstein's World of Mathematics, Graph Path
• Eric Weisstein's World of Mathematics, Grid Graph

Crossrefs

Rows 2-7 are A288516, A288527, A358800, A358801, A358802, A358803.

Main diagonal is A288032.

Cf. A231829, A064298, A271465, A271592, A120443, A001184, A145157, A003763.