A223432 T(n,k)=5X5X5 triangular graph without horizontal edges coloring a rectangular array: number of nXk 0..14 arrays where 0..14 label nodes of a graph with edges 0,1 0,2 1,3 1,4 2,4 2,5 3,6 3,7 4,7 4,8 5,8 5,9 6,10 6,11 7,11 7,12 8,12 8,13 9,13 9,14 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph

15, 40, 40, 120, 248, 120, 356, 1648, 1648, 356, 1088, 11168, 25436, 11168, 1088, 3276, 76384, 394736, 394736, 76384, 3276, 10052, 524736, 6256832, 14270468, 6256832, 524736, 10052, 30380, 3613024, 98783592, 522011152, 522011152, 98783592

Offset

1,1

Comments

Table starts

.....15.........40...........120...............356..................1088

.....40........248..........1648.............11168.................76384

....120.......1648.........25436............394736...............6256832

....356......11168........394736..........14270468.............522011152

...1088......76384.......6256832.........522011152...........44494633876

...3276.....524736......98783592.......19187276496.........3786278496752

..10052....3613024....1575629948......707293805988.......325249041493488

..30380...24906592...24993296408....26110271476744.....27818291732538560

..93296..171802144..399339124688...964706306602248...2394866308625232348

.282240.1185459328.6343618034616.35659725052665944.205161525882369203816

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

k=1: a(n) = 14*a(n-2) -49*a(n-4) +49*a(n-6) for n>7

k=2: a(n) = 14*a(n-1) -57*a(n-2) +28*a(n-3) +225*a(n-4) -230*a(n-5) -192*a(n-6) +232*a(n-7) +28*a(n-8) -48*a(n-9)

k=3: [order 32] for n>33

k=4: [order 71]

Example

Some solutions for n=3 k=4
.11..7..4..7....7..4..7..4....7..4..8.12...11..7..4..1...11..7.11..7
..7.12..7.12....4..1..4..1....3..1..4..7....7..3..7..3....7.12..7.12
..4..7..4..8....1..0..2..4....6..3..7..3....4..1..4..7...12..7.12..8

Crossrefs

Sequence in context: A369720 A369758 A325659 * A044092 A044473 A321491

Adjacent sequences: A223429 A223430 A223431 * A223433 A223434 A223435

Keyword

nonn,tabl

Author

R. H. Hardin Mar 20 2013

Status

approved