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A187166 Number of 5-step self-avoiding walks on an n X n X n cube summed over all starting positions. 2

%I

%S 0,144,3240,14256,37470,77184,137754,223536,338886,488160,675714,

%T 905904,1183086,1511616,1895850,2340144,2848854,3426336,4076946,

%U 4805040,5614974,6511104,7497786,8579376,9760230,11044704,12437154,13941936,15563406

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

%C Row 5 of A187162.

%H R. H. Hardin, <a href="/A187166/b187166.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 726*n^3 - 2640*n^2 + 2688*n - 720 for n>3.

%F Conjectures from _Colin Barker_, Apr 20 2018: (Start)

%F G.f.: 6*x^2*(24 + 444*x + 360*x^2 - 115*x^3 + 4*x^4 + 9*x^5) / (1 - x)^4.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>7.

%F (End)

%e A solution for 2 X 2 X 2:

%e ..5..0.....4..1

%e ..0..0.....3..2

%Y Cf. A187162.

%K nonn,walk

%O 1,2

%A _R. H. Hardin_, Mar 06 2011

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Last modified January 18 17:18 EST 2022. Contains 350455 sequences. (Running on oeis4.)