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A233239 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order 13
1, 2, 3, 6, 19, 11, 23, 271, 313, 48, 99, 4504, 18744, 6046, 236, 452, 79201, 1212549, 1409129, 123352, 1248, 2136, 1419889, 79794804, 338046654, 107709266, 2565169, 6896, 10313, 25622596, 5267525102, 81477098771, 94601758339, 8259321811 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
.......1............2..................6.......................23
.......3...........19................271.....................4504
......11..........313..............18744..................1212549
......48.........6046............1409129................338046654
.....236.......123352..........107709266..............94601758339
....1248......2565169.........8259321811...........26484848685044
....6896.....53692063.......633724470764.........7415057313896849
...39168...1126297996.....48630297616989......2076029517168733114
..226496..23643610702...3731839458899046....581236325493128357679
.1325568.496455294319.286378755661153351.162731637919752077883024
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 12*a(n-1) -44*a(n-2) +48*a(n-3)
k=2: a(n) = 29*a(n-1) -175*a(n-2) +147*a(n-3)
k=3: a(n) = 93*a(n-1) -1273*a(n-2) +1943*a(n-3) -882*a(n-4) +120*a(n-5)
k=4: a(n) = 311*a(n-1) -8722*a(n-2) +10022*a(n-3) -1645*a(n-4) +35*a(n-5)
Empirical for row n:
n=1: a(n) = 9*a(n-1) -23*a(n-2) +15*a(n-3)
n=2: a(n) = 23*a(n-1) -81*a(n-2) -143*a(n-3) +82*a(n-4) +120*a(n-5) for n>6
n=3: [order 9] for n>10
n=4: [order 21] for n>22
EXAMPLE
Some solutions for n=3 k=4
..0..1..0..2....0..0..1..2....0..1..0..2....0..0..1..0....0..0..1..2
..3..3..0..0....4..0..0..3....1..0..0..0....2..0..2..1....2..0..1..5
..0..3..3..4....3..0..4..2....2..2..0..2....2..1..2..2....1..5..3..5
CROSSREFS
Column 1 is A233162(n+1)
Column 2 is A233107
Row 1 is A233106
Sequence in context: A114302 A000304 A000614 * A018290 A364645 A182250
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 06 2013
STATUS
approved

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Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)