A231285 T(n,k)=Number of nXk 0..3 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, and upper left element zero

0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 6, 8, 0, 0, 0, 26, 76, 66, 0, 0, 0, 118, 834, 1170, 400, 0, 0, 0, 522, 9488, 34786, 18208, 2722, 0, 0, 0, 2310, 105962, 1083188, 1400418, 278758, 17688, 0, 0, 0, 10234, 1179364, 31513702, 113949472, 56442770, 4294812, 117026, 0

Offset

1,8

Comments

Table starts

.0.0......0........0...........0...............0..................0

.0.0......2........6..........26.............118................522

.0.0......8.......76.........834............9488.............105962

.0.0.....66.....1170.......34786.........1083188...........31513702

.0.0....400....18208.....1400418.......113949472.........8501873308

.0.0...2722...278758....56442770.....12128733980......2336016267460

.0.0..17688..4294812..2276141330...1290580702666....640923626812310

.0.0.117026.66052162.91775666754.137311555002556.175842069555560942

Links

R. H. Hardin, Table of n, a(n) for n = 1..143

Formula

Empirical for column k:

k=3: a(n) = 4*a(n-1) +17*a(n-2)

k=4: a(n) = 9*a(n-1) +86*a(n-2) +190*a(n-3) -29*a(n-4) +a(n-5)

k=5: [order 10] for n>11

k=6: [order 30] for n>31

k=7: [order 55] for n>57

Empirical for row n:

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

n=3: [order 19] for n>21

Example

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

Crossrefs

Row 2 is A230245(n-1)

Sequence in context: A066503 A057385 A231108 * A268729 A182317 A158801

Adjacent sequences: A231282 A231283 A231284 * A231286 A231287 A231288

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 06 2013

Status

approved