A232589 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or antidiagonally, with no adjacent elements equal.

0, 10, 2, 2, 34, 4, 26, 12, 124, 6, 20, 152, 42, 456, 10, 70, 108, 996, 122, 1686, 18, 90, 690, 606, 6406, 332, 6232, 32, 210, 744, 8104, 3002, 41328, 882, 23034, 56, 336, 3232, 7568, 93236, 14398, 266490, 2322, 85130, 98, 674, 4516, 66744, 68072, 1079300

Offset: 1

Author

R. H. Hardin, Nov 26 2013

Keywords

• nonn
• tabl

Comments

Table starts

...0......10.....2........26.......20...........70..........90.............210

...2......34....12.......152......108..........690.........744............3232

...4.....124....42.......996......606.........8104........7568...........66744

...6.....456...122......6406.....3002........93236.......68072.........1364998

..10....1686...332.....41328....14398......1079300......595304........28339640

..18....6232...882....266490....66950.....12486510.....5045772.......589476500

..32...23034..2322...1718514...306022....144506106....41969054.....12273587770

..56...85130..6092..11082034..1382638...1672314806...344123498....255585490674

..98..314626.15962..71463916..6200520..19353375198..2791211292...5322596390316

.172.1162804.41802.460844060.27671244.223972627480.22459482618.110844512072980

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..477

Formula

Empirical for column k:

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

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

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

k=4: a(n) = 5*a(n-1) +9*a(n-2) +2*a(n-3) +a(n-4) +2*a(n-5)

k=5: [order 14]

k=6: [order 23] for n>27

k=7: [order 44] for n>45

Empirical for row n:

n=1: a(n) = -a(n-1) +2*a(n-2) +4*a(n-3) +3*a(n-4) +a(n-5)

n=2: [order 9] for n>10

n=3: [order 24] for n>26

n=4: [order 49] for n>54