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

Author

R. H. Hardin, Mar 22 2011

Keywords

• nonn

Comments

Row 4 of A188147.

Examples

			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
		

Links

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

Crossrefs

Cf. A188147.

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)