A223335 Rolling cube footprints: number of 6 X n 0..7 arrays starting with 0 where 0..7 label vertices of a cube and every array movement to a horizontal or antidiagonal neighbor moves along a corresponding cube edge.

32768, 177147, 36756909, 7626831723, 1587890407761, 330815891296611, 68935627430614161, 14365712340521444763, 2993767914167348634225, 623894511848537009674251, 130018376961215856234304281

Offset

1,1

Comments

Row 6 of A223331.

Links

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

Formula

Empirical: a(n) = 363*a(n-1) -42090*a(n-2) +2394790*a(n-3) -76949379*a(n-4) +1439989707*a(n-5) -14188685367*a(n-6) +22105928025*a(n-7) +1145452404696*a(n-8) -13381549738272*a(n-9) +56254263011793*a(n-10) +62916731731323*a(n-11) -1574353040753800*a(n-12) +5560131978318054*a(n-13) -1833699655619436*a(n-14) -34189681765260294*a(n-15) +75258675804889728*a(n-16) -6463571598539280*a(n-17) -143095150109785392*a(n-18) +141900806436429312*a(n-19) -28670292192657024*a(n-20) for n>25.

Example

Some solutions for n=3
..0..4..0....0..4..0....0..4..0....0..4..0....0..4..0....0..4..0....0..4..0
..0..4..0....0..4..0....0..4..0....0..4..0....0..4..0....0..4..0....0..4..0
..0..2..6....0..2..6....0..4..0....0..4..6....0..2..6....0..4..6....0..2..0
..6..4..0....3..7..5....0..2..0....6..4..0....6..7..5....6..2..6....6..2..0
..0..1..0....3..1..0....0..1..3....6..2..0....5..4..0....3..2..6....6..2..6
..5..4..5....0..2..0....0..2..0....6..4..6....0..2..3....0..2..6....0..4..0
Vertex neighbors:
0 -> 1 2 4
1 -> 0 3 5
2 -> 0 3 6
3 -> 1 2 7
4 -> 0 5 6
5 -> 1 4 7
6 -> 2 4 7
7 -> 3 5 6

Crossrefs

Cf. A223331.

Sequence in context: A217589 A069276 A195235 * A194934 A016997 A017069

Adjacent sequences: A223332 A223333 A223334 * A223336 A223337 A223338

Keyword

nonn,changed

Author

R. H. Hardin, Mar 19 2013

Status

approved