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A188149
Number of 4-step self-avoiding walks on an n X n square summed over all starting positions.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 22 2011
STATUS
approved