A116903 Seaweeds(n): number of n-step self-avoiding walks on upper two quadrants grid starting at origin.

1, 3, 7, 19, 49, 131, 339, 899, 2345, 6199, 16225, 42811, 112285, 296051, 777411, 2049025, 5384855, 14190509, 37313977, 98324565, 258654441, 681552747, 1793492411, 4725856129, 12439233695, 32778031159, 86295460555, 227399388019, 598784536563, 1577923781445, 4155176578581

Offset: 0

Author

Giovanni Resta, Feb 15 2006

Keywords

• nonn

Comments

These walks remind me of fluctuant seaweeds anchored to the sea bottom.

Examples

			The 19 seaweeds of length 3. X marks the origin = anchor point.
........................................................
O-O-O...O-O.. .O-O...O-O....O..O-O-O...O......O..O-O....
....|.....|.. .|.....|......|..|.......|......|....|....
....X...X-O....O.....O-X....O..X..O-O..O-O....O....O-X..
...............|............|.......|....|....|.........
O-O.....O-O....X....O.......O..O....O....X..X-O.......O.
|.|.....|...........|.......|..|....|.................|.
X.O...X-O.....O-O...O-O-X...X..O....X.....O.........O-O.
..............|.|..............|..........|.........|...
..X-O-O-O.....O.X...O-O-O-X....O-X....X-O-O.........X...
........................................................
		

Links

• M. N. Barber et al., Some tests of scaling theory for a self-avoiding walk attached to a surface, 1978 J. Phys. A: Math. Gen. 11 1833. [_Vladeta Jovovic_, Nov 26 2008]

Crossrefs

Cf. A001411, A038373, A116903.

Extensions

a(23)-a(30) from Scott R. Shannon, Jul 26 2020