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

Author

R. H. Hardin, Dec 06 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A233162(n+1)

Row 1 is A233106

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