A223251 Two-loop graph coloring a rectangular array: number of n X 4 0..4 arrays where 0..4 label nodes of a graph with edges 0,1 1,2 2,0 0,3 3,4 4,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

80, 1076, 17828, 307144, 5359892, 93770308, 1641741608, 28748561780, 503440061060, 8816254627208, 154390919319636, 2703707386173764, 47347570829880040, 829155025056272692, 14520239405020681988

Offset

1,1

Comments

Column 4 of A223255.

Links

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

Formula

Empirical: a(n) = 20*a(n-1) - 28*a(n-2) - 299*a(n-3) + 436*a(n-4) + 476*a(n-5) - 460*a(n-6) for n>7.

Empirical g.f.: 4*x*(20 - 131*x - 363*x^2 + 1158*x^3 + 760*x^4 - 1036*x^5 + 24*x^6) / (1 - 20*x + 28*x^2 + 299*x^3 - 436*x^4 - 476*x^5 + 460*x^6). - Colin Barker, Aug 18 2018

Example

Some solutions for n=3:
..4..0..4..3....2..0..3..0....0..4..0..2....0..3..0..1....3..0..3..0
..0..4..3..4....0..3..0..3....2..0..2..0....1..0..4..0....0..3..0..4
..1..0..4..3....3..0..2..0....0..3..0..1....0..4..0..4....4..0..2..0

Crossrefs

Cf. A223255.

Sequence in context: A203347 A201193 A264129 * A251427 A275701 A168364

Adjacent sequences: A223248 A223249 A223250 * A223252 A223253 A223254

Keyword

nonn

Author

R. H. Hardin, Mar 18 2013

Status

approved