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 A223269 T(n,k)=Rolling cube face footprints: number of nXk 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge 12
 1, 4, 6, 16, 48, 36, 64, 576, 576, 216, 256, 6144, 20992, 6912, 1296, 1024, 67584, 622592, 765952, 82944, 7776, 4096, 737280, 19726336, 63438848, 27951104, 995328, 46656, 16384, 8060928, 611319808, 5889851392, 6467616768, 1020002304, 11943936 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Table starts ....1......4.........16...........64.............256...............1024 ....6.....48........576.........6144...........67584.............737280 ...36....576......20992.......622592........19726336..........611319808 ..216...6912.....765952.....63438848......5889851392.......522106961920 .1296..82944...27951104...6467616768...1771674009600....450204914417664 .7776.995328.1020002304.659411697664.534392715870208.389343801904201728 LINKS R. H. Hardin, Table of n, a(n) for n = 1..311 FORMULA Empirical for column k: k=1: a(n) = 6*a(n-1) k=2: a(n) = 12*a(n-1) k=3: a(n) = 40*a(n-1) -128*a(n-2) k=4: a(n) = 112*a(n-1) -1024*a(n-2) k=5: [order 6] k=6: [order 9] k=7: [order 19] Empirical for row n: n=1: a(n) = 4*a(n-1) n=2: a(n) = 8*a(n-1) +32*a(n-2) n=3: a(n) = 24*a(n-1) +256*a(n-2) -1024*a(n-3) for n>4 n=4: [order 6] for n>7 n=5: [order 10] for n>11 n=6: [order 23] for n>24 EXAMPLE Some solutions for n=3 k=4 ..0..3..1..2....0..1..0..1....0..4..5..1....0..4..2..4....0..2..1..3 ..0..2..4..3....0..3..5..1....0..4..0..3....0..1..0..4....0..3..4..2 ..4..2..1..2....0..2..0..1....3..1..5..4....3..4..0..1....0..3..4..0 Face neighbors: 0.->.1.2.3.4 1.->.0.2.3.5 2.->.0.1.4.5 3.->.0.1.4.5 4.->.0.3.2.5 5.->.1.3.4.2 CROSSREFS Column 1 is A000400(n-1) Column 2 is 4*12^(n-1) Column 3 is A223197 Row 1 is A000302(n-1) Sequence in context: A032295 A072279 A038236 * A264471 A264477 A223357 Adjacent sequences: A223266 A223267 A223268 * A223270 A223271 A223272 KEYWORD nonn,tabl AUTHOR R. H. Hardin Mar 19 2013 STATUS approved

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Last modified February 21 22:50 EST 2024. Contains 370239 sequences. (Running on oeis4.)