cp's OEIS Frontend

A223330 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.

%I A223330 #6 Jul 23 2025 04:00:57
%S A223330 729,453789,283231809,176834343105,110409049892673,68935627430614161,
%T A223330 43041050285035823937,26873361387913413198609,
%U A223330 16778808787792177773698625,10476115000476214621652175825,6540928315682905702406399281857
%N A223330 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 A223330 Column 7 of A223331
%H A223330 R. H. Hardin, <a href="/A223330/b223330.txt">Table of n, a(n) for n = 1..210</a>
%F A223330 Empirical: a(n) = 692*a(n-1) -43569*a(n-2) +847042*a(n-3) -6303164*a(n-4) +15731352*a(n-5)
%e A223330 Some solutions for n=3
%e A223330 ..0..4..0..4..5..4..5....0..4..0..4..6..7..3....0..4..0..4..0..4..0
%e A223330 ..0..4..0..1..5..1..3....0..4..0..2..3..1..5....0..4..0..4..6..2..0
%e A223330 ..0..4..5..4..5..1..5....0..4..6..7..5..7..6....0..4..6..2..6..2..0
%e A223330 Vertex neighbors:
%e A223330 0 -> 1 2 4
%e A223330 1 -> 0 3 5
%e A223330 2 -> 0 3 6
%e A223330 3 -> 1 2 7
%e A223330 4 -> 0 5 6
%e A223330 5 -> 1 4 7
%e A223330 6 -> 2 4 7
%e A223330 7 -> 3 5 6
%K A223330 nonn
%O A223330 1,1
%A A223330 _R. H. Hardin_ Mar 19 2013