A188148 Number of 3-step self-avoiding walks on an n X n square summed over all starting positions.

0, 8, 44, 104, 188, 296, 428, 584, 764, 968, 1196, 1448, 1724, 2024, 2348, 2696, 3068, 3464, 3884, 4328, 4796, 5288, 5804, 6344, 6908, 7496, 8108, 8744, 9404, 10088, 10796, 11528, 12284, 13064, 13868, 14696, 15548, 16424, 17324, 18248, 19196, 20168, 21164

Offset

1,2

Comments

Row 3 of A188147.

Links

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

Formula

Empirical: a(n) = 12*n^2 - 24*n + 8 for n>1.

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

G.f.: 4*x^2*(2 + 5*x - x^2) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.

(End)

Example

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

Crossrefs

Cf. A188147.

Sequence in context: A046377 A075816 A290787 * A316466 A100583 A261996

Adjacent sequences: A188145 A188146 A188147 * A188149 A188150 A188151

Keyword

nonn

Author

R. H. Hardin, Mar 22 2011

Status

approved