A223233 - OEIS

%I #4 Mar 18 2013 20:34:52

%S 1,5,12,25,65,144,125,785,845,1728,625,7445,25225,10985,20736,3125,

%T 75665,492365,812225,142805,248832,15625,753005,11043445,32837285,

%U 26157625,1856465,2985984,78125,7540985,236027705,1697263985,2191464605,842416625

%N T(n,k)=Rolling icosahedron footprints: number of nXk 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an icosahedral edge

%C Table starts

%C ............1.............5................25.................125

%C ...........12............65...............785................7445

%C ..........144...........845.............25225..............492365

%C .........1728.........10985............812225............32837285

%C ........20736........142805..........26157625..........2191464605

%C .......248832.......1856465.........842416625........146259564725

%C ......2985984......24134045.......27130395625.......9761484584045

%C .....35831808.....313742585......873746350625.....651489782832965

%C ....429981696....4078653605....28139386665625...43480983274973885

%C ...5159780352...53022496865...906241361740625.2901957882023749205

%C ..61917364224..689292459245.29185902861015625

%C .743008370688.8960801970185

%H R. H. Hardin, <a href="/A223233/b223233.txt">Table of n, a(n) for n = 1..97</a>

%F Empirical for column k:

%F k=1: a(n) = 12*a(n-1)

%F k=2: a(n) = 13*a(n-1)

%F k=3: a(n) = 35*a(n-1) -90*a(n-2)

%F k=4: a(n) = 73*a(n-1) -423*a(n-2) +351*a(n-3)

%F k=5: [order 11]

%F k=6: [order 26]

%F Empirical for row n:

%F n=1: a(n) = 5*a(n-1)

%F n=2: a(n) = 7*a(n-1) +30*a(n-2) for n>3

%F n=3: a(n) = 18*a(n-1) +103*a(n-2) -552*a(n-3) +540*a(n-4) for n>5

%F n=4: a(n) = [order 12] for n>13

%e Some solutions for n=3 k=4

%e ..0..6..0..5....0..5..6..5....0..7..0..1....0..1..3..1....0..1..0..7

%e ..0..6.10..5....0..5..6..5....3..7..0..7....3..7..3..9....0..7..0..7

%e ..0..5.10..4....6..2..6..5....3..7..5..7....3..9.11..7....3..1..3..7

%e Vertex neighbors:

%e 0 -> 1 2 5 6 7

%e 1 -> 0 2 3 7 8

%e 2 -> 0 1 4 6 8

%e 3 -> 1 7 8 9 11

%e 4 -> 2 6 8 9 10

%e 5 -> 0 6 7 10 11

%e 6 -> 0 2 4 5 10

%e 7 -> 0 1 3 5 11

%e 8 -> 1 2 3 4 9

%e 9 -> 3 4 8 10 11

%e 10 -> 4 5 6 9 11

%e 11 -> 3 5 7 9 10

%Y Column 1 is A001021(n-1)

%Y Column 2 is 5*13^(n-1)

%Y Row 1 is A000351(n-1)

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_ Mar 18 2013