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.

36, 324, 3132, 30564, 298620, 2918052, 28515132, 278649828, 2722966524, 26608833828, 260021573820, 2540931306084, 24829985481084, 242638664618916, 2371065485035068, 23170056359958756, 226417834139125500

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