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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 8
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Mar 19 2013
STATUS
approved

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Last modified July 20 18:59 EDT 2024. Contains 374459 sequences. (Running on oeis4.)