A223339 5X5X5 triangular graph coloring a rectangular array: number of nX3 0..14 arrays where 0..14 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 6,10 6,11 7,11 10,11 7,12 8,12 11,12 11,12 8,13 9,13 12,13 9,14 13,14 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph

264, 6696, 190740, 5514360, 161370036, 4730218284, 138947808456, 4081817304888, 119957730775764, 3525232400391672, 103605465347776488, 3044880491450389068, 89488169170132234404, 2630017284676266897204, 77295354555176007541020

Offset

1,1

Comments

Column 3 of A223344

Links

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

Formula

Empirical: a(n) = 18*a(n-1) +585*a(n-2) -5160*a(n-3) -85485*a(n-4) +505600*a(n-5) +3996404*a(n-6) -19237700*a(n-7) -89239938*a(n-8) +375211256*a(n-9) +1104726794*a(n-10) -4232791939*a(n-11) -8081655126*a(n-12) +29153658888*a(n-13) +35808212649*a(n-14) -125320594701*a(n-15) -95870415823*a(n-16) +336725591045*a(n-17) +149825017362*a(n-18) -554412838812*a(n-19) -124734888118*a(n-20) +531808961051*a(n-21) +43836491896*a(n-22) -268190168640*a(n-23) -2736660827*a(n-24) +57764829598*a(n-25) +504580148*a(n-26) -3286957664*a(n-27) +156627216*a(n-28) +43946272*a(n-29) -3289536*a(n-30)

Example

Some solutions for n=3
..7..4..3....3..7.12...11.12.11....1..3..4....7.12..7....7.11.12....7..8..5
..3..7..4....7..6..7...10.11..6....2..4..1...12..7..3....8.12.11....6..7..8
..7..4..2...12.11..6...11.12.11....4..2..4....7.12..7....7..8..7....3..6..7

Crossrefs

Sequence in context: A092724 A112069 A282781 * A022043 A035315 A288877

Adjacent sequences: A223336 A223337 A223338 * A223340 A223341 A223342

Keyword

nonn

Author

R. H. Hardin Mar 19 2013

Status

approved