A188150 - OEIS

%I #14 Apr 27 2018 09:22:26

%S 0,0,104,432,972,1712,2652,3792,5132,6672,8412,10352,12492,14832,

%T 17372,20112,23052,26192,29532,33072,36812,40752,44892,49232,53772,

%U 58512,63452,68592,73932,79472,85212,91152,97292,103632,110172,116912,123852,130992

%N Number of 5-step self-avoiding walks on an n X n square summed over all starting positions.

%C Row 5 of A188147.

%H R. H. Hardin, <a href="/A188150/b188150.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 100*n^2 - 360*n + 272 for n>3.

%F Conjectures from _Colin Barker_, Apr 27 2018: (Start)

%F G.f.: 4*x^3*(26 + 30*x - 3*x^2 - 3*x^3) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.

%F (End)

%e Some solutions for 3 X 3:

%e   5 4 3   1 0 5   5 0 1   2 1 0   0 1 0   1 0 0   5 0 0

%e   0 1 2   2 3 4   4 3 2   3 4 5   0 2 3   2 0 0   4 3 0

%e   0 0 0   0 0 0   0 0 0   0 0 0   0 5 4   3 4 5   1 2 0

%Y Cf. A188147.

%K nonn

%O 1,3

%A _R. H. Hardin_, Mar 22 2011