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A188148 Number of 3-step self-avoiding walks on an n X n square summed over all starting positions. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 21 12:28 EST 2019. Contains 329370 sequences. (Running on oeis4.)