A231246 T(n,k)=Number of nXk 0..3 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero

0, 0, 0, 0, 2, 0, 0, 14, 6, 0, 0, 44, 78, 20, 0, 0, 146, 464, 552, 68, 0, 0, 572, 3090, 5992, 3820, 230, 0, 0, 2258, 22460, 76264, 76136, 26658, 778, 0, 0, 8660, 162766, 1081934, 1872136, 968824, 185074, 2632, 0, 0, 33026, 1169472, 15270416, 52280836, 46019438

Offset

1,5

Comments

Table starts

.0....0.......0.........0...........0.............0................0

.0....2......14........44.........146...........572.............2258

.0....6......78.......464........3090.........22460...........162766

.0...20.....552......5992.......76264.......1081934.........15270416

.0...68....3820.....76136.....1872136......52280836.......1450042214

.0..230...26658....968824....46019438....2532190370.....138246711032

.0..778..185074..12322784..1130422470..122516675112...13176773912306

.0.2632.1287036.156753000.27772974680.5929632659798.1256579264497704

Links

R. H. Hardin, Table of n, a(n) for n = 1..161

Formula

Empirical for column k:

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

k=3: a(n) = 4*a(n-1) +16*a(n-2) +26*a(n-3) +37*a(n-4) +6*a(n-5)

k=4: a(n) = 10*a(n-1) +30*a(n-2) +53*a(n-3) +71*a(n-4) -a(n-5) +6*a(n-6) -8*a(n-7)

k=5: [order 19]

k=6: [order 74]

Empirical for row n:

n=2: a(n) = 4*a(n-1) -3*a(n-2) +8*a(n-3) +4*a(n-4) for n>5

n=3: [order 7] for n>8

n=4: [order 22] for n>23

n=5: [order 62] for n>63

Example

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

Crossrefs

Column 2 is A231057

Sequence in context: A193294 A231049 A231080 * A216991 A191418 A347093

Adjacent sequences: A231243 A231244 A231245 * A231247 A231248 A231249

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 06 2013

Status

approved