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 A223357 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 or antidiagonal neighbor moves across a corresponding cube edge 10
 1, 4, 6, 16, 64, 36, 64, 768, 1024, 216, 256, 9216, 36864, 16384, 1296, 1024, 110592, 1327104, 1769472, 262144, 7776, 4096, 1327104, 48365568, 191102976, 84934656, 4194304, 46656, 16384, 15925248, 1764753408, 21177040896, 27518828544 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Table starts ....1.......4.........16............64..............256................1024 ....6......64........768..........9216...........110592.............1327104 ...36....1024......36864.......1327104.........48365568..........1764753408 ..216...16384....1769472.....191102976......21177040896.......2356125106176 .1296..262144...84934656...27518828544....9273505480704....3147420753985536 .7776.4194304.4076863488.3962711310336.4060947412942848.4204783428144463872 LINKS R. H. Hardin, Table of n, a(n) for n = 1..241 FORMULA Empirical for column k: k=1: a(n) = 6*a(n-1) k=2: a(n) = 16*a(n-1) k=3: a(n) = 48*a(n-1) k=4: a(n) = 144*a(n-1) k=5: a(n) = 480*a(n-1) -18432*a(n-2) k=6: a(n) = 1600*a(n-1) -368640*a(n-2) +21233664*a(n-3) k=7: a(n) = 5376*a(n-1) -5750784*a(n-2) +2038431744*a(n-3) -217432719360*a(n-4) Empirical for row n: n=1: a(n) = 4*a(n-1) n=2: a(n) = 12*a(n-1) for n>2 n=3: a(n) = 40*a(n-1) -128*a(n-2) for n>4 n=4: a(n) = 144*a(n-1) -3840*a(n-2) +24576*a(n-3) for n>7 n=5: [order 7] for n>11 n=6: [order 9] for n>15 n=7: [order 27] for n>33 EXAMPLE Some solutions for n=3 k=4 ..0..2..0..2....0..3..5..2....0..2..5..4....0..4..0..4....0..1..3..4 ..0..4..0..1....0..3..5..3....0..4..0..1....0..4..0..4....0..1..0..1 ..0..4..5..4....0..1..0..1....0..4..2..1....0..2..0..1....0..1..2..4 CROSSREFS Column 1 is A000400(n-1) Column 2 is A013709 (n-1) Column 3 is 16*48^(n-1) Column 4 is 64*144^(n-1) Row 1 is A000302(n-1) Row 2 is 64*12^(n-2) for n>1 Sequence in context: A223269 A264471 A264477 * A083009 A365111 A190968 Adjacent sequences: A223354 A223355 A223356 * A223358 A223359 A223360 KEYWORD nonn,tabl AUTHOR R. H. Hardin Mar 19 2013 STATUS approved

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Last modified February 25 00:32 EST 2024. Contains 370308 sequences. (Running on oeis4.)