A188785 - OEIS

%I #9 Apr 28 2018 12:49:07

%S 0,64,432,1536,4000,8640,16464,28672,46656,72000,106480,152064,210912,

%T 285376,378000,491520,628864,793152,987696,1216000,1481760,1788864,

%U 2141392,2543616,3000000,3515200,4094064,4741632,5463136,6264000,7149840

%N Number of 2-step self-avoiding walks on an n X n X n X n 4-cube summed over all starting positions.

%C Row 2 of A188784.

%H R. H. Hardin, <a href="/A188785/b188785.txt">Table of n, a(n) for n = 1..43</a>

%F Empirical: a(n) = 8*n^4 - 8*n^3.

%F Conjectures from _Colin Barker_, Apr 28 2018: (Start)

%F G.f.: 16*x^2*(4 + 7*x + x^2) / (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>5.

%F (End)

%Y Cf. A188784.

%K nonn

%O 1,2

%A _R. H. Hardin_, Apr 10 2011