cp's OEIS Frontend

A223282 T(n,k)=Rolling icosahedron face footprints: number of nXk 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

%I A223282 #6 Jul 23 2025 03:57:25
%S A223282 1,3,20,9,15,400,27,87,75,8000,81,351,849,375,160000,243,1575,4995,
%T A223282 8295,1875,3200000,729,6831,38457,72279,81057,9375,64000000,2187,
%U A223282 29943,261819,1024071,1048923,792087,46875,1280000000,6561,130815,1881441,10979127
%N A223282 T(n,k)=Rolling icosahedron face footprints: number of nXk 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.
%C A223282 Table starts
%C A223282 ............1.......3..........9...........27..............81...............243
%C A223282 ...........20......15.........87..........351............1575..............6831
%C A223282 ..........400......75........849.........4995...........38457............261819
%C A223282 .........8000.....375.......8295........72279.........1024071..........10979127
%C A223282 .......160000....1875......81057......1048923........28271577.........473368227
%C A223282 ......3200000....9375.....792087.....15229647.......792881031.......20570223999
%C A223282 .....64000000...46875....7740273....221142771.....22392745881......895927195659
%C A223282 ...1280000000..234375...75637959...3211159815....634400697159....39047604482055
%C A223282 ..25600000000.1171875..739134273..46628577099..17998034165721..1702160040384051
%C A223282 .512000000000.5859375.7222821495.677084057343.510923724667143.74204651599582287
%H A223282 R. H. Hardin, <a href="/A223282/b223282.txt">Table of n, a(n) for n = 1..161</a>
%F A223282 Empirical for column k:
%F A223282 k=1: a(n) = 20*a(n-1)
%F A223282 k=2: a(n) = 5*a(n-1)
%F A223282 k=3: a(n) = 11*a(n-1) -12*a(n-2)
%F A223282 k=4: a(n) = 17*a(n-1) -36*a(n-2)
%F A223282 k=5: a(n) = 45*a(n-1) -518*a(n-2) +1268*a(n-3) +1704*a(n-4) -4064*a(n-5) +1536*a(n-6)
%F A223282 k=6: [order 9]
%F A223282 k=7: [order 20]
%F A223282 Empirical for row n:
%F A223282 n=1: a(n) = 3*a(n-1)
%F A223282 n=2: a(n) = 3*a(n-1) +6*a(n-2) for n>3
%F A223282 n=3: a(n) = 5*a(n-1) +18*a(n-2) -24*a(n-3) for n>4
%F A223282 n=4: a(n) = 5*a(n-1) +92*a(n-2) -56*a(n-3) -920*a(n-4) +192*a(n-5) +1152*a(n-6) for n>7
%F A223282 n=5: [order 12] for n>13
%F A223282 n=6: [order 26] for n>27
%e A223282 Some solutions for n=3 k=4
%e A223282 ..0..5..0..5....0..5..0..5....0..5..0..5....0..2..0..2....0..5..7..5
%e A223282 ..0..2..0..5....0..2..0..5....0..5..0..1....0..2..0..2....7..5..0..5
%e A223282 ..8..2..0..2....3..2..0..1....0..2..0..2....0..5..0..2....9..5..0..2
%e A223282 Face neighbors:
%e A223282 0 -> 1 2 5
%e A223282 1 -> 0 4 6
%e A223282 2 -> 0 3 8
%e A223282 3 -> 2 4 16
%e A223282 4 -> 3 1 17
%e A223282 5 -> 0 7 9
%e A223282 6 -> 1 7 10
%e A223282 7 -> 6 5 11
%e A223282 8 -> 2 9 13
%e A223282 9 -> 8 5 14
%e A223282 10 -> 6 12 17
%e A223282 11 -> 7 12 14
%e A223282 12 -> 11 10 19
%e A223282 13 -> 8 15 16
%e A223282 14 -> 9 11 15
%e A223282 15 -> 14 13 19
%e A223282 16 -> 3 13 18
%e A223282 17 -> 4 10 18
%e A223282 18 -> 16 17 19
%e A223282 19 -> 15 18 12
%Y A223282 Column 1 is A009964(n-1)
%Y A223282 Column 2 is A005053
%Y A223282 Row 1 is A000244(n-1)
%K A223282 nonn,tabl
%O A223282 1,2
%A A223282 _R. H. Hardin_ Mar 19 2013