A223323 - OEIS

A223323

Rolling icosahedron footprints: number of 3 X n 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.

144, 3125, 105625, 3570125, 122039125, 4176940625, 142980696625, 4894441131125, 167544253118125, 5735298712573625, 196328142425559625, 6720615878249268125, 230057073000574997125, 7875209325727694302625, 269580591960578208870625

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OFFSET

1,1

COMMENTS

Row 3 of A223321.

LINKS

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

FORMULA

Empirical: a(n) = 38*a(n-1) - 129*a(n-2) for n>4.

Empirical g.f.: x*(144 - 2347*x + 5451*x^2 - 40500*x^3) / (1 - 38*x + 129*x^2). - Colin Barker, Aug 19 2018

EXAMPLE

Some solutions for n=3:

..0..6..5....0..7..3....0..1..8....0..7.11....0..7.11....0..7..1....0..7..1

..4.10..4....3..8..2....0..1..8....3..7..3....0..7..1....1..2..8....1..8..4

.11..9..3....1..8..1....2..1..2....3..9..8...11..3..7....0..1..7....9..8..4

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

Cf. A223321.

Sequence in context: A231584 A367702 A221695 * A251433 A223300 A330837

Adjacent sequences: A223320 A223321 A223322 * A223324 A223325 A223326

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 19 2013

STATUS

approved