cp's OEIS Frontend

A188148 Number of 3-step self-avoiding walks on an n X n square summed over all starting positions.

%I A188148 #10 Apr 26 2018 11:32:55
%S A188148 0,8,44,104,188,296,428,584,764,968,1196,1448,1724,2024,2348,2696,
%T A188148 3068,3464,3884,4328,4796,5288,5804,6344,6908,7496,8108,8744,9404,
%U A188148 10088,10796,11528,12284,13064,13868,14696,15548,16424,17324,18248,19196,20168,21164
%N A188148 Number of 3-step self-avoiding walks on an n X n square summed over all starting positions.
%C A188148 Row 3 of A188147.
%H A188148 R. H. Hardin, <a href="/A188148/b188148.txt">Table of n, a(n) for n = 1..50</a>
%F A188148 Empirical: a(n) = 12*n^2 - 24*n + 8 for n>1.
%F A188148 Conjectures from _Colin Barker_, Apr 26 2018: (Start)
%F A188148 G.f.: 4*x^2*(2 + 5*x - x^2) / (1 - x)^3.
%F A188148 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.
%F A188148 (End)
%e A188148 Some solutions for 3 X 3:
%e A188148 ..0..3..0....0..0..0....0..1..0....1..0..0....0..1..0....0..0..0....0..3..0
%e A188148 ..0..2..0....0..3..0....0..2..3....2..0..0....0..2..0....3..2..1....0..2..1
%e A188148 ..0..1..0....0..2..1....0..0..0....3..0..0....0..3..0....0..0..0....0..0..0
%Y A188148 Cf. A188147.
%K A188148 nonn
%O A188148 1,2
%A A188148 _R. H. Hardin_, Mar 22 2011