A233217 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally 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, 23, 11, 23, 376, 452, 48, 99, 7222, 35446, 10313, 236, 452, 147019, 3054973, 3638416, 249062, 1248, 2136, 3054973, 268289572, 1340889772, 380283286, 6147803, 6896, 10313, 63927526, 23644611625, 496475792293, 591021089923, 39892988056

Offset

1,2

Comments

Table starts

....1.........2.............6.................23.....................99

....3........23...........376...............7222.................147019

...11.......452.........35446............3054973..............268289572

...48.....10313.......3638416.........1340889772...........496475792293

..236....249062.....380283286.......591021089923........919538740854193

.1248...6147803...39892988056....260625046992322....1703198747507336644

.6896.152986472.4187991850726.114934898294104873.3154729081272072714436

Links

R. H. Hardin, Table of n, a(n) for n = 1..161

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) = 35*a(n-1) -259*a(n-2) +225*a(n-3)

k=3: a(n) = 127*a(n-1) -2331*a(n-2) +2205*a(n-3)

k=4: a(n) = 491*a(n-1) -22099*a(n-2) +21609*a(n-3)

k=5: a(n) = 1975*a(n-1) -228357*a(n-2) +1804281*a(n-3) -4170978*a(n-4) +2593080*a(n-5)

k=6: [order 7]

k=7: [order 11]

Empirical for row n:

n=1: a(n) = 9*a(n-1) -23*a(n-2) +15*a(n-3)

n=2: a(n) = 29*a(n-1) -175*a(n-2) +147*a(n-3) for n>4

n=3: a(n) = 111*a(n-1) -2128*a(n-2) +10532*a(n-3) -17559*a(n-4) +9045*a(n-5) for n>7

n=4: [order 9] for n>12

n=5: [order 19] for n>23

n=6: [order 42] for n>47

Example

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

Crossrefs

Column 1 is A233162(n+1)

Row 1 is A233106

Sequence in context: A303584 A261014 A000616 * A261963 A183179 A018300

Adjacent sequences: A233214 A233215 A233216 * A233218 A233219 A233220

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 06 2013

Status

approved