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

0,2

Comments

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

Links

Table of n, a(n) for n=0..30.

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]

Example

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...
........................................................

Crossrefs

Cf. A001411, A038373, A116903.

Sequence in context: A061646 A017926 A017927 * A298416 A151266 A147234

Adjacent sequences: A116900 A116901 A116902 * A116904 A116905 A116906

Keyword

nonn

Author

Giovanni Resta, Feb 15 2006

Extensions

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

Status

approved