A230614 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 8, 30, 0, 0, 0, 0, 30, 260, 348, 0, 0, 0, 0, 108, 2358, 7072, 3956, 0, 0, 0, 0, 386, 20430, 149664, 186396, 44916, 0, 0, 0, 0, 1376, 176774, 3023532, 9244260, 4899200, 509978, 0, 0, 0, 0, 4902, 1527918, 61203362

Offset

1,12

Comments

Table starts

.0.0.0.......0..........0.............0................0..................0

.0.0.0.......2..........8............30..............108................386

.0.0.0......30........260..........2358............20430.............176774

.0.0.0.....348.......7072........149664..........3023532...........61203362

.0.0.0....3956.....186396.......9244260........434369516........20503681466

.0.0.0...44916....4899200.....570014364......62312057642......6859445695566

.0.0.0..509978..128706852...35145166536....8937075346246...2294186499807542

.0.0.0.5790456.3381000336.2166884610178.1281770005911328.767293632652220616

Links

R. H. Hardin, Table of n, a(n) for n = 1..239

Formula

Empirical for column k:

k=4: a(n) = 15*a(n-1) -45*a(n-2) +42*a(n-3) -12*a(n-4) +a(n-5)

k=5: a(n) = 31*a(n-1) -126*a(n-2) +42*a(n-3) +79*a(n-4) -a(n-5) +8*a(n-6) for n>7

k=6: [order 22] for n>23

k=7: [order 39] for n>41

Empirical for row n:

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

n=3: [order 14] for n>17

n=4: [order 59] for n>63

Example

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

Crossrefs

Row 2 is A230269(n-1)

Sequence in context: A350731 A364055 A184366 * A230730 A299905 A225783

Adjacent sequences: A230611 A230612 A230613 * A230615 A230616 A230617

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 25 2013

Status

approved