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%I #10 Apr 26 2018 11:37:37
%S 0,8,80,232,456,752,1120,1560,2072,2656,3312,4040,4840,5712,6656,7672,
%T 8760,9920,11152,12456,13832,15280,16800,18392,20056,21792,23600,
%U 25480,27432,29456,31552,33720,35960,38272,40656,43112,45640,48240,50912,53656
%N Number of 4-step self-avoiding walks on an n X n square summed over all starting positions.
%C Row 4 of A188147.
%H R. H. Hardin, <a href="/A188149/b188149.txt">Table of n, a(n) for n = 1..50</a>
%F Empirical: a(n) = 36*n^2 - 100*n + 56 for n>2.
%F Conjectures from _Colin Barker_, Apr 26 2018: (Start)
%F G.f.: 8*x^2*(1 + 7*x + 2*x^2 - x^3) / (1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>5.
%F (End)
%e Some solutions for 3 X 3:
%e ..0..0..0....0..0..1....1..0..0....3..2..0....4..1..0....0..0..0....1..0..0
%e ..0..2..1....0..3..2....2..0..0....4..1..0....3..2..0....4..0..0....2..3..4
%e ..0..3..4....0..4..0....3..4..0....0..0..0....0..0..0....3..2..1....0..0..0
%Y Cf. A188147.
%K nonn
%O 1,2
%A _R. H. Hardin_, Mar 22 2011
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