A293177 Triangle read by rows: T(m,n) = number of maximal independent sets in m X n rectangular grid graph (m>=1, 1<=n<=m).

1, 2, 2, 2, 4, 10, 3, 6, 18, 42, 4, 10, 38, 108, 358, 5, 16, 78, 274, 1132, 4468, 7, 26, 156, 692, 3580, 17742, 88056, 9, 42, 320, 1754, 11382, 70616, 439338, 2745186, 12, 68, 654, 4442, 36270, 281202, 2192602, 17155374, 16, 110, 1326, 11248, 114992, 1117442, 10912392, 106972582

Offset

1,2

Links

Table of n, a(n) for n=1..52.

Oh, Seungsang. "Maximal independent sets on a grid graph." Discrete Mathematics 340.12 (2017): 2762-2768. Also arXiv:1709.03678.

Eric Weisstein's World of Mathematics, Grid Graph

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

Example

Triangle begins:
1,
2,2,
2,4,10,
3,6,18,42,
4,10,38,108,358,
5,16,78,274,1132,4468,
7,26,156,692,3580,17742,88056,
9,42,320,1754,11382,70616,439338,2745186,
12,68,654,4442,36270,281202,2192602,17155374,
16,110,1326,11248,114992,1117442,10912392,106972582,
...

Crossrefs

Main diagonal is A197048.

Rows 3,4,5,6,... form the beginnings of A197049, A197050, A197051, A197052, ..., respectively.

Triangular version of A197054.

Sequence in context: A021822 A153986 A199889 * A231382 A360314 A213270

Adjacent sequences: A293174 A293175 A293176 * A293178 A293179 A293180

Keyword

nonn,tabl

Author

N. J. A. Sloane, Oct 19 2017

Status

approved