A233239 - OEIS

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

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

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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

R. H. Hardin, Table of n, a(n) for n = 1..127

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

Adjacent sequences: A233236 A233237 A233238 * A233240 A233241 A233242

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 06 2013

STATUS

approved