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A223361 Rolling cube footprints: number of 6Xn 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or antidiagonal neighbor moves across a corresponding cube edge.

%I A223361 #6 Jul 23 2025 04:02:59
%S A223361 7776,4194304,4076863488,3962711310336,4060947412942848,
%T A223361 4204783428144463872,4387933871654786039808,4591848540270748206366720,
%U A223361 4812465805493379433041494016,5046647918221316806981151883264
%N A223361 Rolling cube footprints: number of 6Xn 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or antidiagonal neighbor moves across a corresponding cube edge.
%C A223361 Row 6 of A223357
%H A223361 R. H. Hardin, <a href="/A223361/b223361.txt">Table of n, a(n) for n = 1..210</a>
%F A223361 Empirical: a(n) = 1920*a(n-1) -1159168*a(n-2) +272105472*a(n-3) -9613344768*a(n-4) -7199438929920*a(n-5) +1446957302153216*a(n-6) -121544413380870144*a(n-7) +4845873199050653696*a(n-8) -74363437047141629952*a(n-9) for n>15
%e A223361 Some solutions for n=3
%e A223361 ..0..3..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0
%e A223361 ..0..3..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0
%e A223361 ..0..3..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0
%e A223361 ..1..2..4....1..3..5....5..3..0....0..1..0....1..2..1....0..3..1....0..4..0
%e A223361 ..1..2..1....5..4..3....0..3..1....2..4..0....1..0..4....4..3..1....0..2..0
%e A223361 ..1..0..3....2..0..1....0..2..4....0..3..4....4..2..0....5..2..5....5..1..5
%K A223361 nonn
%O A223361 1,1
%A A223361 _R. H. Hardin_ Mar 19 2013