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A223234 Rolling icosahedron footprints: number of 2 X n 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an icosahedral edge. 1
12, 65, 785, 7445, 75665, 753005, 7540985, 75377045, 753868865, 7538393405, 75384819785, 753845540645, 7538463378065, 75384609865805, 753846170402585, 7538461488792245, 75384615533623265, 753846153399130205 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 2 of A223233.

LINKS

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

FORMULA

Empirical: a(n) = 7*a(n-1) + 30*a(n-2) for n>3.

Conjectures from Colin Barker, Aug 17 2018: (Start)

G.f.: x*(12 - 19*x - 30*x^2) / ((1 + 3*x)*(1 - 10*x)).

a(n) = (-25*(-1)^n*3^(1+n) + 49*10^n) / 65 for n>1.

(End)

EXAMPLE

Some solutions for n=3:

..0..2..1....0..7.11....0..6..2....0..6..5....0..7..3....0..2..1....0..2..0

..0..7..0....3..7..3...10..6..4....4..6..5....3..7..0....6..2..8....8..2..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. A223233.

Sequence in context: A232383 A003868 A304833 * A289223 A296914 A285580

Adjacent sequences:  A223231 A223232 A223233 * A223235 A223236 A223237

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 18 2013

STATUS

approved

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Last modified September 23 12:11 EDT 2021. Contains 347617 sequences. (Running on oeis4.)