cp's OEIS Frontend

A188149 Number of 4-step self-avoiding walks on an n X n square summed over all starting positions.

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