cp's OEIS Frontend

A223332 Rolling cube footprints: number of 3 X n 0..7 arrays starting with 0 where 0..7 label vertices of a cube and every array movement to a horizontal or antidiagonal neighbor moves along a corresponding cube edge.

%I A223332 #10 Aug 19 2018 10:42:02
%S A223332 64,243,3969,64827,1059723,17324685,283231809,4630406067,75700050363,
%T A223332 1237579942725,20232537609249,330771018512907,5407599817782603,
%U A223332 88405979220238365,1445302430884160289,23628482316968449347
%N A223332 Rolling cube footprints: number of 3 X n 0..7 arrays starting with 0 where 0..7 label vertices of a cube and every array movement to a horizontal or antidiagonal neighbor moves along a corresponding cube edge.
%C A223332 Row 3 of A223331.
%H A223332 R. H. Hardin, <a href="/A223332/b223332.txt">Table of n, a(n) for n = 1..210</a>
%F A223332 Empirical: a(n) = 18*a(n-1) - 27*a(n-2) for n>4.
%F A223332 Conjectures from _Colin Barker_, Aug 19 2018: (Start)
%F A223332 G.f.: x*(64 - 909*x + 1323*x^2 - 54*x^3) / (1 - 18*x + 27*x^2).
%F A223332 a(n) = (49/54)*((9-3*sqrt(6))^n + (3*(3+sqrt(6)))^n) for n>2.
%F A223332 (End)
%e A223332 Some solutions for n=3:
%e A223332   0 2 6    0 4 6    0 2 6    0 1 5    0 2 3    0 1 5    0 2 6
%e A223332   6 7 6    6 2 3    3 7 5    5 4 6    3 7 6    5 7 3    0 4 0
%e A223332   3 7 6    6 2 0    6 4 6    6 2 0    6 7 3    6 7 6    6 4 6
%e A223332 Vertex neighbors:
%e A223332   0 -> 1 2 4
%e A223332   1 -> 0 3 5
%e A223332   2 -> 0 3 6
%e A223332   3 -> 1 2 7
%e A223332   4 -> 0 5 6
%e A223332   5 -> 1 4 7
%e A223332   6 -> 2 4 7
%e A223332   7 -> 3 5 6
%Y A223332 Cf. A223331.
%K A223332 nonn
%O A223332 1,1
%A A223332 _R. H. Hardin_, Mar 19 2013