A223348 3 X 3 X 3 triangular graph without horizontal edges coloring a rectangular array: number of n X 4 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,3 1,4 2,4 2,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
60, 1076, 20836, 405988, 7918948, 154482340, 3013692516, 58792282660, 1146943179236, 22375024222628, 436500886445412, 8515433203445028, 166122463695945956, 3240783209292085412, 63222490059635217508
Offset: 1
Keywords
Examples
Some solutions for n=3: ..1..4..1..3....2..0..1..0....1..4..2..4....5..2..0..1....4..2..4..2 ..4..2..0..1....4..2..0..1....0..2..4..2....2..0..1..3....1..4..2..4 ..1..0..1..0....1..4..1..3....2..0..2..4....0..1..0..1....4..2..0..2
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A223352.
Formula
Empirical: a(n) = 23*a(n-1) - 66*a(n-2) - 52*a(n-3) + 208*a(n-4) + 32*a(n-5) - 128*a(n-6).
Empirical g.f.: 4*x*(1 - 4*x)*(15 - 16*x - 52*x^2 + 16*x^3 + 32*x^4) / (1 - 23*x + 66*x^2 + 52*x^3 - 208*x^4 - 32*x^5 + 128*x^6). - Colin Barker, Aug 19 2018
Comments