cp's OEIS Frontend

A223186 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.

%I A223186 #6 Jun 07 2021 15:07:25
%S A223186 1,5,5,25,20,25,125,80,80,125,625,320,400,320,625,3125,1280,2080,2080,
%T A223186 1280,3125,15625,5120,10880,14560,10880,5120,15625,78125,20480,56960,
%U A223186 103520,103520,56960,20480,78125,390625,81920,298240,738720,1018720
%N A223186 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 A223186 Table starts
%C A223186 ........1........5.........25.........125...........625.............3125
%C A223186 ........5.......20.........80.........320..........1280.............5120
%C A223186 .......25.......80........400........2080.........10880............56960
%C A223186 ......125......320.......2080.......14560........103520...........738720
%C A223186 ......625.....1280......10880......103520.......1018720.........10117600
%C A223186 .....3125.....5120......56960......738720......10117600........141047120
%C A223186 ....15625....20480.....298240.....5274720.....100734400.......1978496760
%C A223186 ....78125....81920....1561600....37664800....1003652480......27809548920
%C A223186 ...390625...327680....8176640...268947680...10001217120.....391129835720
%C A223186 ..1953125..1310720...42813440..1920431520...99661921440....5502120113200
%C A223186 ..9765625..5242880..224174080.13712917600..993129226400...77403634963000
%C A223186 .48828125.20971520.1173790720.97917648160.9896517562400.1088923059178480
%H A223186 R. H. Hardin, <a href="/A223186/b223186.txt">Table of n, a(n) for n = 1..199</a>
%F A223186 Empirical for column k:
%F A223186 k=1: a(n) = 5*a(n-1)
%F A223186 k=2: a(n) = 4*a(n-1)
%F A223186 k=3: a(n) = 6*a(n-1) -4*a(n-2) for n>3
%F A223186 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 A223186 k=5: [order 12] for n>14
%F A223186 k=6: [order 34] for n>37
%F A223186 k=7: [order 88] for n>93
%e A223186 Some solutions for n=3, k=4
%e A223186 ..0..7..5.10....0..6..2..0....0..7..3.11....0..6..2..8....0..7..1..3
%e A223186 ..5..0..6..5....2..4..6..2....5.11..7..5....5..0..1..2....1..0..7..1
%e A223186 ..6..5..0..7....6..2..0..1...10..5.11.10....6..2..0..1....7..1..3..8
%e A223186 Vertex neighbors:
%e A223186 0 -> 1 2 5 6 7
%e A223186 1 -> 0 2 3 7 8
%e A223186 2 -> 0 1 4 6 8
%e A223186 3 -> 1 7 8 9 11
%e A223186 4 -> 2 6 8 9 10
%e A223186 5 -> 0 6 7 10 11
%e A223186 6 -> 0 2 4 5 10
%e A223186 7 -> 0 1 3 5 11
%e A223186 8 -> 1 2 3 4 9
%e A223186 9 -> 3 4 8 10 11
%e A223186 10 -> 4 5 6 9 11
%e A223186 11 -> 3 5 7 9 10
%Y A223186 Column 1 is A000351(n-1).
%Y A223186 Column 2 is A003947.
%K A223186 nonn,tabl
%O A223186 1,2
%A A223186 _R. H. Hardin_ Mar 18 2013