A233147 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally, antidiagonally 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, 16, 6, 23, 225, 225, 23, 99, 3727, 13259, 3727, 99, 452, 65120, 845917, 845917, 65120, 452, 2136, 1158334, 54777233, 198313130, 54777233, 1158334, 2136, 10313, 20726079, 3556749764, 46648134615, 46648134615, 3556749764, 20726079

Offset

1,2

Comments

Table starts

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

......2...........16...............225....................3727

......6..........225.............13259..................845917

.....23.........3727............845917...............198313130

.....99........65120..........54777233.............46648134615

....452......1158334........3556749764..........10976545771938

...2136.....20726079......231058112982........2582927810338210

..10313....371568349....15011638934832......607799571521107132

..50469...6665506622...975308641633714...143023917159921251486

.249062.119595908140.63366149608139911.33655571006177475521033

Links

R. H. Hardin, Table of n, a(n) for n = 1..144

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) = 25*a(n-1) -134*a(n-2) +134*a(n-3) -25*a(n-4) +a(n-5)

k=3: [order 10] for n>11

k=4: [order 27] for n>28

Example

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

Crossrefs

Column 1 is A233106

Sequence in context: A330798 A260687 A083555 * A336633 A001464 A067136

Adjacent sequences: A233144 A233145 A233146 * A233148 A233149 A233150

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 04 2013

Status

approved