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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 16 13:32 EDT 2019. Contains 328093 sequences. (Running on oeis4.)