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R. H. Hardin, <a href="/A233147/b233147.txt">Table of n, a(n) for n = 1..144</a>

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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

1,2

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

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

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

Column 1 is A233106

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nonn,tabl

R. H. Hardin, Dec 04 2013

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