A223325 Rolling icosahedron footprints: number of 5Xn 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge

20736, 1953125, 446265625, 101966340125, 24143758634125, 5759605530667625, 1379464144963464625, 330817503041200989125, 79372689616849936523125, 19046505898852803312046625, 4570642727979496865778147625

Offset

1,1

Comments

Row 5 of A223321

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 410*a(n-1) -51839*a(n-2) +2998354*a(n-3) -88929070*a(n-4) +1198807214*a(n-5) +2889121905*a(n-6) -340756682572*a(n-7) +4538793109678*a(n-8) -13887817317962*a(n-9) -242674670034177*a(n-10) +2612400275589524*a(n-11) -4250937817051838*a(n-12) -72579353969012690*a(n-13) +404852006352195731*a(n-14) +294243010726671144*a(n-15) -8038059311698199807*a(n-16) +14527240098893219908*a(n-17) +63207106281330811172*a(n-18) -241285400707856322796*a(n-19) -99441316590244134158*a(n-20) +1499939986936247507922*a(n-21) -1264768034332853154292*a(n-22) -3709575277042038429058*a(n-23) +6249708500546392632287*a(n-24) +1712083980241985550010*a(n-25) -7806673210840206689815*a(n-26) +1552725322135658220450*a(n-27) +3587994096679078794377*a(n-28) -1272290169371896871744*a(n-29) -473135759143977735225*a(n-30) +224855787210470741790*a(n-31) -20543329382473731600*a(n-32) for n>36

Example

Some solutions for n=3
..0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0
..0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0
..0..5..7....0..5..7....0..6..5....0..1..0....0..7..3....0..5.10....0..7..0
..0..5..6...10.11..7....4..6..5....0..6..5...11..9..4...10..6..0....1..7..1
..6..0..7....5.11.10...10..6..0....4..6..0...10..9..8....0..1..7...11..3..9
Vertex neighbors:
0 -> 1 2 5 6 7
1 -> 0 2 3 7 8
2 -> 0 1 4 6 8
3 -> 1 7 8 9 11
4 -> 2 6 8 9 10
5 -> 0 6 7 10 11
6 -> 0 2 4 5 10
7 -> 0 1 3 5 11
8 -> 1 2 3 4 9
9 -> 3 4 8 10 11
10 -> 4 5 6 9 11
11 -> 3 5 7 9 10

Crossrefs

Sequence in context: A223237 A017404 A017524 * A180691 A103282 A013865

Adjacent sequences: A223322 A223323 A223324 * A223326 A223327 A223328

Keyword

nonn

Author

R. H. Hardin Mar 19 2013

Status

approved