A232908 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

0, 10, 4, 52, 34, 8, 82, 320, 194, 12, 432, 2958, 4928, 1034, 32, 2372, 27692, 68310, 62276, 4986, 84, 8456, 250934, 1825972, 1827866, 761860, 24498, 184, 29970, 2338508, 39641548, 115154048, 49501666, 9880580, 122994, 412, 132972, 21159320

Offset

1,2

Comments

Table starts

....0.......10...........52..............82.................432

....4.......34..........320............2958...............27692

....8......194.........4928...........68310.............1825972

...12.....1034........62276.........1827866...........115154048

...32.....4986.......761860........49501666..........7517844304

...84....24498......9880580......1295371950........485354122160

..184...122994....123587140.....34359557398......31320663237216

..412...613658...1571314692....911287659098....2024849938767040

..976..3048362..19864803028..24111990771426..130826030730696144

.2276.15169602.251467184100.638690599346926.8452502440791870368

Links

R. H. Hardin, Table of n, a(n) for n = 1..127

Formula

Empirical for column k:

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

k=2: a(n) = 4*a(n-1) -a(n-2) +26*a(n-3) +16*a(n-4)

k=3: [order 8]

k=4: [order 18]

k=5: [order 34] for n>35

k=6: [order 75] for n>77

Empirical for row n:

n=1: a(n) = 4*a(n-2) +28*a(n-3) +80*a(n-4) +48*a(n-5) -67*a(n-6) -228*a(n-7) -224*a(n-8)

n=2: [order 29] for n>30

Example

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

Crossrefs

Sequence in context: A094580 A192027 A180866 * A216653 A267180 A038306

Adjacent sequences: A232905 A232906 A232907 * A232909 A232910 A232911

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 02 2013

Status

approved