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A223299 4 X 4 X 4 triangular graph coloring a rectangular array: number of n X 2 0..9 arrays where 0..9 label nodes of a graph with edges 0,1 0,2 1,2 1,3 1,4 2,4 3,4 2,5 4,5 3,6 3,7 4,7 6,7 4,8 5,8 7,8 5,9 8,9 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph. 1
36, 324, 3132, 30564, 298620, 2918052, 28515132, 278649828, 2722966524, 26608833828, 260021573820, 2540931306084, 24829985481084, 242638664618916, 2371065485035068, 23170056359958756, 226417834139125500 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 2 of A223305.

LINKS

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

FORMULA

Empirical: a(n) = 11*a(n-1) - 12*a(n-2).

Conjectures from Colin Barker, Aug 19 2018: (Start)

G.f.: 36*x*(1 - 2*x) / (1 - 11*x + 12*x^2).

a(n) = (3*2^(-n)*((11-sqrt(73))^n*(-1+sqrt(73)) + (1+sqrt(73))*(11+sqrt(73))^n)) / sqrt(73).

(End)

EXAMPLE

Some solutions for n=3:

..0..2....2..0....8..9....5..4....7..8....0..2....4..8....3..4....3..4....1..3

..2..5....4..1....4..5....9..8....4..7....1..0....2..5....4..2....1..2....0..1

..5..2....1..2....1..4....5..9....7..3....0..2....1..2....8..4....2..1....1..3

CROSSREFS

Cf. A223305.

Sequence in context: A014800 A213124 A067473 * A068075 A219004 A053136

Adjacent sequences:  A223296 A223297 A223298 * A223300 A223301 A223302

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 19 2013

STATUS

approved

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Last modified June 13 11:17 EDT 2021. Contains 344990 sequences. (Running on oeis4.)