A288026 Array read by antidiagonals: T(m,n) = number of maximal matchings in the grid graph P_m X P_n.

1, 1, 1, 2, 2, 2, 2, 5, 5, 2, 3, 11, 22, 11, 3, 4, 24, 75, 75, 24, 4, 5, 51, 264, 400, 264, 51, 5, 7, 109, 941, 2357, 2357, 941, 109, 7, 9, 234, 3286, 13407, 22228, 13407, 3286, 234, 9, 12, 503, 11623, 76667, 207423, 207423, 76667, 11623, 503, 12

Offset

1,4

Links

Andrew Howroyd, Table of n, a(n) for n = 1..276

Eric Weisstein's World of Mathematics, Grid Graph

Eric Weisstein's World of Mathematics, Maximal Independent Edge Set

Example

Table starts:
=====================================================
m\n| 1   2    3     4       5        6          7
---|-------------------------------------------------
1  | 1   1    2     2       3        4          5 ...
2  | 1   2    5    11      24       51        109 ...
3  | 2   5   22    75     264      941       3286 ...
4  | 2  11   75   400    2357    13407      76667 ...
5  | 3  24  264  2357   22228   207423    1922112 ...
6  | 4  51  941 13407  207423  3136370   47256485 ...
7  | 5 109 3286 76667 1922112 47256485 1158560776 ...
...

Crossrefs

Main diagonal is A287595.

Rows 1-3 are A182097(n+2), A286945, A288028.

Cf. A210662, A099390, A286912, A288025.

Sequence in context: A333505 A177333 A118486 * A141299 A035681 A195601

Adjacent sequences: A288023 A288024 A288025 * A288027 A288028 A288029

Keyword

nonn,tabl

Author

Andrew Howroyd, Jun 04 2017

Status

approved