A188149 Number of 4-step self-avoiding walks on an n X n square summed over all starting positions.

0, 8, 80, 232, 456, 752, 1120, 1560, 2072, 2656, 3312, 4040, 4840, 5712, 6656, 7672, 8760, 9920, 11152, 12456, 13832, 15280, 16800, 18392, 20056, 21792, 23600, 25480, 27432, 29456, 31552, 33720, 35960, 38272, 40656, 43112, 45640, 48240, 50912, 53656

Offset

1,2

Comments

Row 4 of A188147.

Links

R. H. Hardin, Table of n, a(n) for n = 1..50

Formula

Empirical: a(n) = 36*n^2 - 100*n + 56 for n>2.

Conjectures from Colin Barker, Apr 26 2018: (Start)

G.f.: 8*x^2*(1 + 7*x + 2*x^2 - x^3) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>5.

(End)

Example

Some solutions for 3 X 3:
..0..0..0....0..0..1....1..0..0....3..2..0....4..1..0....0..0..0....1..0..0
..0..2..1....0..3..2....2..0..0....4..1..0....3..2..0....4..0..0....2..3..4
..0..3..4....0..4..0....3..4..0....0..0..0....0..0..0....3..2..1....0..0..0

Crossrefs

Cf. A188147.

Sequence in context: A061477 A069543 A144410 * A164755 A050799 A100431

Adjacent sequences: A188146 A188147 A188148 * A188150 A188151 A188152

Keyword

nonn

Author

R. H. Hardin, Mar 22 2011

Status

approved