A232839 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, diagonally or antidiagonally

4, 16, 16, 216, 312, 64, 710, 6664, 3720, 240, 3648, 67718, 168688, 44832, 988, 25642, 1051216, 4836036, 5659896, 500516, 3964, 139456, 17686598, 202470104, 391884166, 179149960, 5809256, 15844, 683250, 265341016, 8873311108, 45851030856

Offset

1,1

Comments

Table starts

.......4...........16.............216...............710...............3648

......16..........312............6664.............67718............1051216

......64.........3720..........168688...........4836036..........202470104

.....240........44832.........5659896.........391884166........45851030856

.....988.......500516.......179149960.......32297599754.....10331973738132

....3964......5809256......5458025808.....2586501812600...2255412540732792

...15844.....71242892....172736599272...210721854104134.504907550840069764

...63808....828231244...5399804456824.17102998113711722

..256096...9665239984.168429228245712

.1029152.115029333056

Links

R. H. Hardin, Table of n, a(n) for n = 1..71

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +10*a(n-2) +11*a(n-3) -a(n-4) -28*a(n-5) -32*a(n-6)

k=2: [order 13]

k=3: [order 38]

Empirical for row n:

n=1: [linear recurrence of order 8]

n=2: [order 33]

Example

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

Crossrefs

Column 1 is A232425

Sequence in context: A202680 A263568 A009570 * A140299 A119007 A043052

Adjacent sequences: A232836 A232837 A232838 * A232840 A232841 A232842

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 30 2013

Status

approved