A223387 T(n,k)=Number of nXk 0..2 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..2 introduced in row major order

1, 2, 2, 5, 9, 5, 14, 57, 57, 14, 41, 366, 777, 366, 41, 122, 2358, 10830, 10830, 2358, 122, 365, 15204, 151962, 329840, 151962, 15204, 365, 1094, 98052, 2136444, 10139432, 10139432, 2136444, 98052, 1094, 3281, 632376, 30053580, 312609528, 684434305

Offset

1,2

Comments

Table starts

.....1..........2..............5.................14.....................41

.....2..........9.............57................366...................2358

.....5.........57............777..............10830.................151962

....14........366..........10830.............329840...............10139432

....41.......2358.........151962...........10139432..............684434305

...122......15204........2136444..........312609528............46377822217

...365......98052.......30053580.........9647052880..........3146553746804

..1094.....632376......422837280.......297793167360........213569806424579

..3281....4078488.....5949375984......9193379042784......14497860201301485

..9842...26304144....83709684792....283823521300032.....984209549790487316

.29525..169648272..1177827765240...8762451963477680...66815578146284698253

.88574.1094144736.16572513858312.270523002967477744.4535968556179629648389

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

k=2: a(n) = 8*a(n-1) -10*a(n-2) for n>3

k=3: a(n) = 19*a(n-1) -72*a(n-2) +34*a(n-3) +44*a(n-4) for n>5

k=4: [order 9] for n>10

k=5: [order 23] for n>24

Example

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

Crossrefs

Column 1 is A007051(n-1)

Sequence in context: A274065 A233073 A275266 * A278386 A262614 A184296

Adjacent sequences: A223384 A223385 A223386 * A223388 A223389 A223390

Keyword

nonn,tabl

Author

R. H. Hardin Mar 19 2013

Status

approved