# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a223331 Showing 1-1 of 1 %I A223331 #4 Mar 19 2013 12:03:17 %S A223331 1,3,8,9,27,64,27,189,243,512,81,1323,3969,2187,4096,243,9261,64827, %T A223331 83349,19683,32768,729,64827,1059723,3176523,1750329,177147,262144, %U A223331 2187,453789,17324685,121264857,155649627,36756909,1594323,2097152,6561 %N 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 %C A223331 Table starts %C A223331 .........1..........3.............9................27....................81 %C A223331 .........8.........27...........189..............1323..................9261 %C A223331 ........64........243..........3969.............64827...............1059723 %C A223331 .......512.......2187.........83349...........3176523.............121264857 %C A223331 ......4096......19683.......1750329.........155649627...........13876429707 %C A223331 .....32768.....177147......36756909........7626831723.........1587890407761 %C A223331 ....262144....1594323.....771895089......373714754427.......181703507374179 %C A223331 ...2097152...14348907...16209796869....18312022966923.....20792470582897209 %C A223331 ..16777216..129140163..340405734249...897289125379227...2379298227030964827 %C A223331 .134217728.1162261467.7148520419229.43967167143582123.272264906211251105313 %C A223331 Horizontal or vertical instead of horizontal or antidiagonal gives A222444 %H A223331 R. H. Hardin, Table of n, a(n) for n = 1..199 %F A223331 Empirical for column k: %F A223331 k=1: a(n) = 8*a(n-1) %F A223331 k=2: a(n) = 9*a(n-1) %F A223331 k=3: a(n) = 21*a(n-1) %F A223331 k=4: a(n) = 49*a(n-1) %F A223331 k=5: a(n) = 117*a(n-1) -294*a(n-2) %F A223331 k=6: a(n) = 282*a(n-1) -3969*a(n-2) +9604*a(n-3) %F A223331 k=7: a(n) = 692*a(n-1) -43569*a(n-2) +847042*a(n-3) -6303164*a(n-4) +15731352*a(n-5) %F A223331 Empirical for row n: %F A223331 n=1: a(n) = 3*a(n-1) %F A223331 n=2: a(n) = 7*a(n-1) for n>2 %F A223331 n=3: a(n) = 18*a(n-1) -27*a(n-2) for n>4 %F A223331 n=4: a(n) = 48*a(n-1) -402*a(n-2) +1064*a(n-3) -789*a(n-4) for n>7 %F A223331 n=5: [order 9] for n>13 %F A223331 n=6: [order 20] for n>25 %F A223331 n=7: [order 51] for n>57 %e A223331 Some solutions for n=3 k=4 %e A223331 ..0..4..5..1....0..4..0..1....0..4..6..4....0..2..0..4....0..4..6..4 %e A223331 ..5..4..0..1....5..1..5..1....0..2..0..2....6..2..6..4....6..2..6..7 %e A223331 ..6..2..3..1....5..7..3..2....3..2..3..1....6..4..0..4....0..2..6..7 %e A223331 Vertex neighbors: %e A223331 0 -> 1 2 4 %e A223331 1 -> 0 3 5 %e A223331 2 -> 0 3 6 %e A223331 3 -> 1 2 7 %e A223331 4 -> 0 5 6 %e A223331 5 -> 1 4 7 %e A223331 6 -> 2 4 7 %e A223331 7 -> 3 5 6 %Y A223331 Column 1 is A001018(n-1) %Y A223331 Column 2 is A013708(n-1) %Y A223331 Column 3 is 9*21^(n-1) %Y A223331 Column 4 is 27*49^(n-1) %Y A223331 Row 1 is A000244(n-1) %Y A223331 Row 2 is 27*7^(n-2) for n>1 %K A223331 nonn,tabl %O A223331 1,2 %A A223331 _R. H. Hardin_ Mar 19 2013 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE