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

1,2

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

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

Example

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

Crossrefs

Sequence in context: A351306 A265994 A201278 * A010175 A363839 A323421

Adjacent sequences: A232586 A232587 A232588 * A232590 A232591 A232592

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 26 2013

Status

approved