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 A223331 T(n,k)=Rolling cube footprints: number of nXk 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 10
 1, 3, 8, 9, 27, 64, 27, 189, 243, 512, 81, 1323, 3969, 2187, 4096, 243, 9261, 64827, 83349, 19683, 32768, 729, 64827, 1059723, 3176523, 1750329, 177147, 262144, 2187, 453789, 17324685, 121264857, 155649627, 36756909, 1594323, 2097152, 6561 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Table starts .........1..........3.............9................27....................81 .........8.........27...........189..............1323..................9261 ........64........243..........3969.............64827...............1059723 .......512.......2187.........83349...........3176523.............121264857 ......4096......19683.......1750329.........155649627...........13876429707 .....32768.....177147......36756909........7626831723.........1587890407761 ....262144....1594323.....771895089......373714754427.......181703507374179 ...2097152...14348907...16209796869....18312022966923.....20792470582897209 ..16777216..129140163..340405734249...897289125379227...2379298227030964827 .134217728.1162261467.7148520419229.43967167143582123.272264906211251105313 Horizontal or vertical instead of horizontal or antidiagonal gives A222444 LINKS R. H. Hardin, Table of n, a(n) for n = 1..199 FORMULA Empirical for column k: k=1: a(n) = 8*a(n-1) k=2: a(n) = 9*a(n-1) k=3: a(n) = 21*a(n-1) k=4: a(n) = 49*a(n-1) k=5: a(n) = 117*a(n-1) -294*a(n-2) k=6: a(n) = 282*a(n-1) -3969*a(n-2) +9604*a(n-3) k=7: a(n) = 692*a(n-1) -43569*a(n-2) +847042*a(n-3) -6303164*a(n-4) +15731352*a(n-5) Empirical for row n: n=1: a(n) = 3*a(n-1) n=2: a(n) = 7*a(n-1) for n>2 n=3: a(n) = 18*a(n-1) -27*a(n-2) for n>4 n=4: a(n) = 48*a(n-1) -402*a(n-2) +1064*a(n-3) -789*a(n-4) for n>7 n=5: [order 9] for n>13 n=6: [order 20] for n>25 n=7: [order 51] for n>57 EXAMPLE Some solutions for n=3 k=4 ..0..4..5..1....0..4..0..1....0..4..6..4....0..2..0..4....0..4..6..4 ..5..4..0..1....5..1..5..1....0..2..0..2....6..2..6..4....6..2..6..7 ..6..2..3..1....5..7..3..2....3..2..3..1....6..4..0..4....0..2..6..7 Vertex neighbors: 0 -> 1 2 4 1 -> 0 3 5 2 -> 0 3 6 3 -> 1 2 7 4 -> 0 5 6 5 -> 1 4 7 6 -> 2 4 7 7 -> 3 5 6 CROSSREFS Column 1 is A001018(n-1) Column 2 is A013708(n-1) Column 3 is 9*21^(n-1) Column 4 is 27*49^(n-1) Row 1 is A000244(n-1) Row 2 is 27*7^(n-2) for n>1 Sequence in context: A167344 A025615 A297324 * A101720 A093439 A000927 Adjacent sequences:  A223328 A223329 A223330 * A223332 A223333 A223334 KEYWORD nonn,tabl AUTHOR R. H. Hardin Mar 19 2013 STATUS approved

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Last modified June 25 03:46 EDT 2022. Contains 354835 sequences. (Running on oeis4.)