login
Rolling cube footprints: number of nX7 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
1

%I #4 Mar 19 2013 12:02:29

%S 729,453789,283231809,176834343105,110409049892673,68935627430614161,

%T 43041050285035823937,26873361387913413198609,

%U 16778808787792177773698625,10476115000476214621652175825,6540928315682905702406399281857

%N Rolling cube footprints: number of nX7 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 Column 7 of A223331

%H R. H. Hardin, <a href="/A223330/b223330.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 692*a(n-1) -43569*a(n-2) +847042*a(n-3) -6303164*a(n-4) +15731352*a(n-5)

%e Some solutions for n=3

%e ..0..4..0..4..5..4..5....0..4..0..4..6..7..3....0..4..0..4..0..4..0

%e ..0..4..0..1..5..1..3....0..4..0..2..3..1..5....0..4..0..4..6..2..0

%e ..0..4..5..4..5..1..5....0..4..6..7..5..7..6....0..4..6..2..6..2..0

%e Vertex neighbors:

%e 0 -> 1 2 4

%e 1 -> 0 3 5

%e 2 -> 0 3 6

%e 3 -> 1 2 7

%e 4 -> 0 5 6

%e 5 -> 1 4 7

%e 6 -> 2 4 7

%e 7 -> 3 5 6

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 19 2013