A360920 Array read by antidiagonals: T(m,n) is the maximum number of vertices in an induced tree in the grid graph P_m X P_n.
1, 2, 2, 3, 3, 3, 4, 5, 5, 4, 5, 6, 7, 6, 5, 6, 8, 9, 9, 8, 6, 7, 9, 12, 12, 12, 9, 7, 8, 11, 14, 15, 15, 14, 11, 8, 9, 12, 16, 18, 19, 18, 16, 12, 9, 10, 14, 18, 21, 22, 22, 21, 18, 14, 10, 11, 15, 21, 24, 26, 26, 26, 24, 21, 15, 11, 12, 17, 23, 27, 30, 31, 31, 30, 27, 23, 17, 12
Offset: 1
Examples
Array begins: =============================================== m\n| 1 2 3 4 5 6 7 8 9 10 11 12 ... -----+----------------------------------------- 1 | 1 2 3 4 5 6 7 8 9 10 11 12 ... 2 | 2 3 5 6 8 9 11 12 14 15 17 18 ... 3 | 3 5 7 9 12 14 16 18 21 23 25 27 ... 4 | 4 6 9 12 15 18 21 24 27 30 33 36 ... 5 | 5 8 12 15 19 22 26 30 34 37 41 44 ... 6 | 6 9 14 18 22 26 31 35 39 44 48 52 ... 7 | 7 11 16 21 26 31 36 41 46 51 56 61 ... 8 | 8 12 18 24 30 35 41 46 52 58 63 69 ... 9 | 9 14 21 27 34 39 46 52 59 65 71 78 ... 10 | 10 15 23 30 37 44 51 58 65 72 79 86 ... 11 | 11 17 25 33 41 48 56 63 71 79 87 94 ... 12 | 12 18 27 36 44 52 61 69 78 86 94 102 ... ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..435
- Eric Weisstein's World of Mathematics, Grid Graph.
Formula
T(m,n) = T(n,m).
Comments