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A360199
Array read by antidiagonals: T(m,n) is the number of induced paths in the grid graph P_m X P_n.
8
0, 1, 1, 3, 8, 3, 6, 25, 25, 6, 10, 58, 94, 58, 10, 15, 117, 270, 270, 117, 15, 21, 218, 681, 1004, 681, 218, 21, 28, 387, 1597, 3330, 3330, 1597, 387, 28, 36, 666, 3592, 10224, 14864, 10224, 3592, 666, 36, 45, 1123, 7880, 29924, 61165, 61165, 29924, 7880, 1123, 45
OFFSET
1,4
COMMENTS
Paths of length zero are not counted here.
LINKS
Eric Weisstein's World of Mathematics, Grid Graph.
Wikipedia, Induced path.
EXAMPLE
Array begins:
============================================================
m\n| 1 2 3 4 5 6 7 8 ...
---+--------------------------------------------------------
1 | 0 1 3 6 10 15 21 28 ...
2 | 1 8 25 58 117 218 387 666 ...
3 | 3 25 94 270 681 1597 3592 7880 ...
4 | 6 58 270 1004 3330 10224 29924 85036 ...
5 | 10 117 681 3330 14864 61165 238897 907148 ...
6 | 15 218 1597 10224 61165 334536 1723535 8647932 ...
7 | 21 387 3592 29924 238897 1723535 11546874 75134416 ...
8 | 28 666 7880 85036 907148 8647932 75134416 629381852 ...
...
CROSSREFS
Main diagonal is A360200.
Rows 1..2 are A000217(n-1), A360201.
Cf. A287151 (induced connected subgraphs), A288518 (undirected paths), A360196 (induced cycles), A360202 (induced trees), A360916 (maximum induced paths).
Sequence in context: A015136 A179450 A333287 * A360851 A117240 A151857
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Jan 29 2023
STATUS
approved