A223362 - OEIS

A223362

Rolling cube footprints: number of 7Xn 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 #4 Mar 19 2013 13:54:38

%S 46656,67108864,195689447424,570630428688384,1778325505192230912,

%T 5617417467128419713024,17937911731045128424390656,

%U 57521864635406651506997329920,184928520804269688527323467350016

%N Rolling cube footprints: number of 7Xn 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 Row 7 of A223357

%H R. H. Hardin, <a href="/A223362/b223362.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7040*a(n-1) -17465344*a(n-2) +18800967680*a(n-3) -5309116448768*a(n-4) -7749529751257088*a(n-5) +8887216147871563776*a(n-6) -3856931134576087007232*a(n-7) +531878790929751511924736*a(n-8) +190513388777369932266471424*a(n-9) -93741331145837409444827234304*a(n-10) +12222651524429752285684779974656*a(n-11) +1263810026656038306032296239562752*a(n-12) -551654242165579114325543159492247552*a(n-13) +43085332629682837240804749191541686272*a(n-14) +4872287652438761570329355653127757365248*a(n-15) -1026508698180612029879031419004744959524864*a(n-16) +28871206910743184105746848222880083247890432*a(n-17) +6540175709583032206058076985272862827184390144*a(n-18) -575371596066692387006645352028057086492317581312*a(n-19) -2523619228901320906565606486887706533101261815808*a(n-20) +2349623641089498925710775976637864762211733222719488*a(n-21) -95152890975475098118298655640034501348474058126131200*a(n-22) -1267975436522094077386825701907323687325172579365289984*a(n-23) +199392037012347758180468057735634758937394385475357114368*a(n-24) -6056422377501992768232187451298021893661257010869595799552*a(n-25) +80033047126180179738906315145897746805305031916916440039424*a(n-26) -401734511064747568885490523085290650630550748445698208825344*a(n-27) for n>33

%e Some solutions for n=3

%e ..0..3..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 19 2013