A223263 - OEIS

%I #4 Mar 19 2013 06:34:00

%S 1,5,5,25,65,25,125,845,845,125,625,10985,28885,10985,625,3125,142805,

%T 988625,988625,142805,3125,15625,1856465,33841585,89405945,33841585,

%U 1856465,15625,78125,24134045,1158447605,8093320565,8093320565

%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 or vertical neighbor moves along an icosahedral edge

%C Table starts

%C .....1.........5............25..............125..................625

%C .....5........65...........845............10985...............142805

%C ....25.......845.........28885...........988625.............33841585

%C ...125.....10985........988625.........89405945...........8093320565

%C ...625....142805......33841585.......8093320565........1940359745365

%C ..3125...1856465....1158447605.....732779276465......465517850602985

%C .15625..24134045...39655444525...66349405785905...111705181963446505

%C .78125.313742585.1357467150905.6007647236699705.26806081975380034085

%H R. H. Hardin, <a href="/A223263/b223263.txt">Table of n, a(n) for n = 1..144</a>

%F Empirical for column k:

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

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

%F k=3: a(n) = 38*a(n-1) -129*a(n-2)

%F k=4: a(n) = 118*a(n-1) -2675*a(n-2) +17534*a(n-3) -37105*a(n-4) +10948*a(n-5) +20013*a(n-6)

%F k=5: [order 20]

%e Some solutions for n=3 k=4

%e ..0..5..6..2....0..6..5..7....0..7..5..0....0..6..0..7....0..2..1..0

%e ..6..0..2..0....6..4..6..5....6..5.10..5....6.10..5..0....6..0..7..1

%e ..0..7..0..1....0..6..5..0....0..7..5..0...10..6.10..5....4..6..0..2

%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 A000351(n-1)

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

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_ Mar 19 2013