A188789 - OEIS

%I #9 Apr 30 2018 11:19:10

%S 0,4224,174720,1141248,3974784,10183872,21725776,41004288,70869216,

%T 114616384,175987632,259170816,368799808,509954496,688160784,

%U 909390592,1180061856,1507038528,1897630576,2359593984,2901130752,3530888896

%N Number of 6-step self-avoiding walks on an n X n X n X n 4-cube summed over all starting positions.

%C Row 6 of A188784.

%H R. H. Hardin, <a href="/A188789/b188789.txt">Table of n, a(n) for n = 1..43</a>

%F Empirical: a(n) = 18584*n^4 - 82552*n^3 + 119616*n^2 - 64320*n + 9984 for n>4.

%F Conjectures from _Colin Barker_, Apr 29 2018: (Start)

%F G.f.: 16*x^2*(264 + 9600*x + 19368*x^2 - 1656*x^3 - 228*x^4 + 697*x^5 - 137*x^6 - 32*x^7) / (1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>8.

%F (End)

%Y Cf. A188784.

%K nonn

%O 1,2

%A _R. H. Hardin_, Apr 10 2011