cp's OEIS Frontend

A187169 Number of 8-step self-avoiding walks on an n X n X n cube summed over all starting positions.

%I A187169 #15 Mar 05 2022 22:12:00
%S A187169 0,144,67824,608928,2188608,5299056,10416624,18026640,28617228,
%T A187169 42676728,60693480,83155824,110552100,143370648,182099808,227227920,
%U A187169 279243324,338634360,405889368,481496688,565944660,659721624,763315920,877215888
%N A187169 Number of 8-step self-avoiding walks on an n X n X n cube summed over all starting positions.
%C A187169 Row 8 of A187162.
%H A187169 R. H. Hardin, <a href="/A187169/b187169.txt">Table of n, a(n) for n = 1..50</a>
%F A187169 Empirical: a(n) = 81390*n^3 - 463074*n^2 + 801216*n - 418032 for n>6.
%F A187169 Conjectures from _Colin Barker_, Apr 21 2018: (Start)
%F A187169 G.f.: 12*x^2*(12 + 5604*x + 28208*x^2 + 13272*x^3 - 6080*x^4 - 1320*x^5 + 748*x^6 + 233*x^7 + 18*x^8) / (1 - x)^4.
%F A187169 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>10.
%F A187169 (End)
%e A187169 A solution for 3 X 3 X 3:
%e A187169 ..0..8..0.....2..7..0.....3..0..0
%e A187169 ..0..0..0.....1..6..0.....4..5..0
%e A187169 ..0..0..0.....0..0..0.....0..0..0
%Y A187169 Cf. A187162.
%K A187169 nonn,walk
%O A187169 1,2
%A A187169 _R. H. Hardin_, Mar 06 2011