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A223182 Rolling icosahedron footprints: number of n X 4 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. 1
125, 320, 2080, 14560, 103520, 738720, 5274720, 37664800, 268947680, 1920431520, 13712917600, 97917648160, 699184991200, 4992559175840, 35649574015840, 254557248560160, 1817676496339680, 12979193733707680, 92678466337073760 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 4 of A223186.

LINKS

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

FORMULA

Empirical: 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.

Empirical g.f.: 5*x*(25 - 186*x + 401*x^2 - 548*x^3 + 280*x^4 - 36*x^5) / ((1 - x)*(1 - 9*x + 16*x^2 - 20*x^3 + 4*x^4)). - Colin Barker, Aug 17 2018

EXAMPLE

Some solutions for n=3:

..0..5..7.11....0..5.10.11....0..5..7..0....0..6..2..0....0..5.10.11

..7.11..3..7....7.11..5.10....7.11..5..7....2..0..1..7....7.11..9.10

..5..7..1..3....5..7.11..5....3..7..0..5....1..7..0..1....5.10..4..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

Cf. A223186.

Sequence in context: A172460 A338469 A253226 * A256362 A175486 A250579

Adjacent sequences:  A223179 A223180 A223181 * A223183 A223184 A223185

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 18 2013

STATUS

approved

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Last modified October 2 08:34 EDT 2022. Contains 357191 sequences. (Running on oeis4.)