A223186 - OEIS

%I #6 Jun 07 2021 15:07:25

%S 1,5,5,25,20,25,125,80,80,125,625,320,400,320,625,3125,1280,2080,2080,

%T 1280,3125,15625,5120,10880,14560,10880,5120,15625,78125,20480,56960,

%U 103520,103520,56960,20480,78125,390625,81920,298240,738720,1018720

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

%C Table starts

%C ........1........5.........25.........125...........625.............3125

%C ........5.......20.........80.........320..........1280.............5120

%C .......25.......80........400........2080.........10880............56960

%C ......125......320.......2080.......14560........103520...........738720

%C ......625.....1280......10880......103520.......1018720.........10117600

%C .....3125.....5120......56960......738720......10117600........141047120

%C ....15625....20480.....298240.....5274720.....100734400.......1978496760

%C ....78125....81920....1561600....37664800....1003652480......27809548920

%C ...390625...327680....8176640...268947680...10001217120.....391129835720

%C ..1953125..1310720...42813440..1920431520...99661921440....5502120113200

%C ..9765625..5242880..224174080.13712917600..993129226400...77403634963000

%C .48828125.20971520.1173790720.97917648160.9896517562400.1088923059178480

%H R. H. Hardin, <a href="/A223186/b223186.txt">Table of n, a(n) for n = 1..199</a>

%F Empirical for column k:

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

%F k=2: a(n) = 4*a(n-1)

%F k=3: a(n) = 6*a(n-1) -4*a(n-2) for n>3

%F k=4: a(n) = 10*a(n-1) -25*a(n-2) +36*a(n-3) -24*a(n-4) +4*a(n-5) for n>6

%F k=5: [order 12] for n>14

%F k=6: [order 34] for n>37

%F k=7: [order 88] for n>93

%e Some solutions for n=3, k=4

%e ..0..7..5.10....0..6..2..0....0..7..3.11....0..6..2..8....0..7..1..3

%e ..5..0..6..5....2..4..6..2....5.11..7..5....5..0..1..2....1..0..7..1

%e ..6..5..0..7....6..2..0..1...10..5.11.10....6..2..0..1....7..1..3..8

%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 A003947.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_ Mar 18 2013