A233230 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally, diagonally, 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, 14, 6, 23, 174, 174, 23, 99, 2541, 8231, 2541, 99, 452, 39203, 420948, 420948, 39203, 452, 2136, 616454, 21895530, 72049266, 21895530, 616454, 2136, 10313, 9757236, 1142726121, 12389989684, 12389989684, 1142726121, 9757236, 10313

Offset

1,2

Comments

Table starts

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

......2..........14..............174...................2541

......6.........174.............8231.................420948

.....23........2541...........420948...............72049266

.....99.......39203.........21895530............12389989684

....452......616454.......1142726121..........2131764323784

...2136.....9757236......59679029456........366805442634477

..10313...154782591....3117164734533......63115455429961173

..50469..2457231917..162820623245643...10860156414181066717

.249062.39019481264.8504746957840386.1868686679256045815893

Links

R. H. Hardin, Table of n, a(n) for n = 1..112

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) = 21*a(n-1) -79*a(n-2) -41*a(n-3) +72*a(n-4) +28*a(n-5)

k=3: [order 10]

k=4: [order 23]

Example

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

Crossrefs

Column 1 is A233106

Sequence in context: A049952 A019100 A019101 * A320070 A319866 A266007

Adjacent sequences: A233227 A233228 A233229 * A233231 A233232 A233233

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 06 2013

Status

approved