A233113 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order

1, 2, 2, 6, 19, 6, 23, 313, 313, 23, 99, 6046, 24912, 6046, 99, 452, 123352, 2154065, 2154065, 123352, 452, 2136, 2565169, 189286871, 794723482, 189286871, 2565169, 2136, 10313, 53692063, 16683923848, 294285758398, 294285758398, 16683923848

Offset

1,2

Comments

Table starts

....1........2.............6................23.....................99

....2.......19...........313..............6046.................123352

....6......313.........24912...........2154065..............189286871

...23.....6046.......2154065.........794723482...........294285758398

...99...123352.....189286871......294285758398........457873555330159

..452..2565169...16683923848...109015274761891.....712427482567592092

.2136.53692063.1471365099497.40385221182281560.1108502928092713640626

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=1: a(n) = 9*a(n-1) -23*a(n-2) +15*a(n-3)

k=2: a(n) = 29*a(n-1) -175*a(n-2) +147*a(n-3)

k=3: a(n) = 111*a(n-1) -2128*a(n-2) +10532*a(n-3) -17559*a(n-4) +9045*a(n-5)

k=4: [order 7]

k=5: [order 15]

Example

Some solutions for n=3 k=4
..0..0..0..1....0..0..0..1....0..0..0..1....0..0..0..1....0..0..0..0
..0..2..2..5....1..1..0..2....1..0..4..2....2..4..2..5....0..0..1..0
..0..2..1..2....2..1..1..5....0..1..3..1....4..0..0..3....2..2..0..1

Crossrefs

Sequence in context: A357537 A173098 A370836 * A366731 A341380 A171694

Adjacent sequences: A233110 A233111 A233112 * A233114 A233115 A233116

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 04 2013

Status

approved